The Minimal Volume of Simplices Containing a Convex Body
Abstract Let %$K \subset {\mathbb {R}}^n%$ be a convex body with barycenter at the origin. We show there is a simplex %$S \subset K%$ having also barycenter at the origin such that %$(\frac{\text {vol}(S)}{\text {vol}(K)})^{1/n} \ge \frac{c}{\sqrt{n}},%$ where %$c>0%$ is an absolute constant. Thi...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Galicer, Daniel [verfasserIn] |
|---|
| Format: |
E-Artikel |
|---|---|
| Sprache: |
Englisch |
| Erschienen: |
2018 |
|---|
| Schlagwörter: |
|---|
| Anmerkung: |
© Mathematica Josephina, Inc. 2018 |
|---|
| Übergeordnetes Werk: |
Enthalten in: The journal of geometric analysis - New York, NY : Springer, 1991, 29(2018), 1 vom: 24. Apr., Seite 717-732 |
|---|---|
| Übergeordnetes Werk: |
volume:29 ; year:2018 ; number:1 ; day:24 ; month:04 ; pages:717-732 |
| Links: |
|---|
| DOI / URN: |
10.1007/s12220-018-0016-4 |
|---|
| Katalog-ID: |
SPR025411764 |
|---|
| LEADER | 01000caa a22002652 4500 | ||
|---|---|---|---|
| 001 | SPR025411764 | ||
| 003 | DE-627 | ||
| 005 | 20230403070429.0 | ||
| 007 | cr uuu---uuuuu | ||
| 008 | 201007s2018 xx |||||o 00| ||eng c | ||
| 024 | 7 | |a 10.1007/s12220-018-0016-4 |2 doi | |
| 035 | |a (DE-627)SPR025411764 | ||
| 035 | |a (SPR)s12220-018-0016-4-e | ||
| 040 | |a DE-627 |b ger |c DE-627 |e rakwb | ||
| 041 | |a eng | ||
| 100 | 1 | |a Galicer, Daniel |e verfasserin |4 aut | |
| 245 | 1 | 4 | |a The Minimal Volume of Simplices Containing a Convex Body |
| 264 | 1 | |c 2018 | |
| 336 | |a Text |b txt |2 rdacontent | ||
| 337 | |a Computermedien |b c |2 rdamedia | ||
| 338 | |a Online-Ressource |b cr |2 rdacarrier | ||
| 500 | |a © Mathematica Josephina, Inc. 2018 | ||
| 520 | |a Abstract Let %$K \subset {\mathbb {R}}^n%$ be a convex body with barycenter at the origin. We show there is a simplex %$S \subset K%$ having also barycenter at the origin such that %$(\frac{\text {vol}(S)}{\text {vol}(K)})^{1/n} \ge \frac{c}{\sqrt{n}},%$ where %$c>0%$ is an absolute constant. This is achieved using stochastic geometric techniques. Precisely, if K is in isotropic position, we present a method to find centered simplices verifying the above bound that works with extremely high probability. By duality, given a convex body %$K \subset {\mathbb {R}}^n%$ we show there is a simplex S enclosing Kwith the same barycenter such that vol(S)vol(K)1/n≤dn,%$\begin{aligned} \left( \frac{\text {vol}(S)}{\text {vol}(K)}\right) ^{1/n} \le d \sqrt{n}, \end{aligned}%$for some absolute constant %$d>0%$. Up to the constant, the estimate cannot be lessened. | ||
| 650 | 4 | |a Volume ratio |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Simplices |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Convex bodies |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Isotropic position |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Random simplices |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Merzbacher, Mariano |4 aut | |
| 700 | 1 | |a Pinasco, Damián |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t The journal of geometric analysis |d New York, NY : Springer, 1991 |g 29(2018), 1 vom: 24. Apr., Seite 717-732 |w (DE-627)496971867 |w (DE-600)2199635-0 |x 1559-002X |7 nnns |
| 773 | 1 | 8 | |g volume:29 |g year:2018 |g number:1 |g day:24 |g month:04 |g pages:717-732 |
| 856 | 4 | 0 | |u https://dx.doi.org/10.1007/s12220-018-0016-4 |z lizenzpflichtig |3 Volltext |
| 912 | |a GBV_USEFLAG_A | ||
| 912 | |a SYSFLAG_A | ||
| 912 | |a GBV_SPRINGER | ||
| 912 | |a GBV_ILN_11 | ||
| 912 | |a GBV_ILN_20 | ||
| 912 | |a GBV_ILN_22 | ||
| 912 | |a GBV_ILN_23 | ||
| 912 | |a GBV_ILN_24 | ||
| 912 | |a GBV_ILN_31 | ||
| 912 | |a GBV_ILN_32 | ||
| 912 | |a GBV_ILN_39 | ||
| 912 | |a GBV_ILN_40 | ||
| 912 | |a GBV_ILN_60 | ||
| 912 | |a GBV_ILN_62 | ||
| 912 | |a GBV_ILN_63 | ||
| 912 | |a GBV_ILN_65 | ||
| 912 | |a GBV_ILN_69 | ||
| 912 | |a GBV_ILN_70 | ||
| 912 | |a GBV_ILN_73 | ||
| 912 | |a GBV_ILN_74 | ||
| 912 | |a GBV_ILN_90 | ||
| 912 | |a GBV_ILN_95 | ||
| 912 | |a GBV_ILN_100 | ||
| 912 | |a GBV_ILN_105 | ||
| 912 | |a GBV_ILN_110 | ||
| 912 | |a GBV_ILN_120 | ||
| 912 | |a GBV_ILN_138 | ||
| 912 | |a GBV_ILN_150 | ||
| 912 | |a GBV_ILN_151 | ||
| 912 | |a GBV_ILN_152 | ||
| 912 | |a GBV_ILN_161 | ||
| 912 | |a GBV_ILN_170 | ||
| 912 | |a GBV_ILN_171 | ||
| 912 | |a GBV_ILN_187 | ||
| 912 | |a GBV_ILN_213 | ||
| 912 | |a GBV_ILN_224 | ||
| 912 | |a GBV_ILN_230 | ||
| 912 | |a GBV_ILN_250 | ||
| 912 | |a GBV_ILN_281 | ||
| 912 | |a GBV_ILN_285 | ||
| 912 | |a GBV_ILN_293 | ||
| 912 | |a GBV_ILN_370 | ||
| 912 | |a GBV_ILN_602 | ||
| 912 | |a GBV_ILN_636 | ||
| 912 | |a GBV_ILN_702 | ||
| 912 | |a GBV_ILN_2001 | ||
| 912 | |a GBV_ILN_2003 | ||
| 912 | |a GBV_ILN_2004 | ||
| 912 | |a GBV_ILN_2005 | ||
| 912 | |a GBV_ILN_2006 | ||
| 912 | |a GBV_ILN_2007 | ||
| 912 | |a GBV_ILN_2008 | ||
| 912 | |a GBV_ILN_2009 | ||
| 912 | |a GBV_ILN_2010 | ||
| 912 | |a GBV_ILN_2011 | ||
| 912 | |a GBV_ILN_2014 | ||
| 912 | |a GBV_ILN_2015 | ||
| 912 | |a GBV_ILN_2020 | ||
| 912 | |a GBV_ILN_2021 | ||
| 912 | |a GBV_ILN_2025 | ||
| 912 | |a GBV_ILN_2026 | ||
| 912 | |a GBV_ILN_2027 | ||
| 912 | |a GBV_ILN_2031 | ||
| 912 | |a GBV_ILN_2034 | ||
| 912 | |a GBV_ILN_2037 | ||
| 912 | |a GBV_ILN_2038 | ||
| 912 | |a GBV_ILN_2039 | ||
| 912 | |a GBV_ILN_2044 | ||
| 912 | |a GBV_ILN_2048 | ||
| 912 | |a GBV_ILN_2049 | ||
| 912 | |a GBV_ILN_2050 | ||
| 912 | |a GBV_ILN_2055 | ||
| 912 | |a GBV_ILN_2057 | ||
| 912 | |a GBV_ILN_2059 | ||
| 912 | |a GBV_ILN_2061 | ||
| 912 | |a GBV_ILN_2064 | ||
| 912 | |a GBV_ILN_2065 | ||
| 912 | |a GBV_ILN_2068 | ||
| 912 | |a GBV_ILN_2070 | ||
| 912 | |a GBV_ILN_2086 | ||
| 912 | |a GBV_ILN_2088 | ||
| 912 | |a GBV_ILN_2093 | ||
| 912 | |a GBV_ILN_2106 | ||
| 912 | |a GBV_ILN_2107 | ||
| 912 | |a GBV_ILN_2108 | ||
| 912 | |a GBV_ILN_2110 | ||
| 912 | |a GBV_ILN_2111 | ||
| 912 | |a GBV_ILN_2112 | ||
| 912 | |a GBV_ILN_2113 | ||
| 912 | |a GBV_ILN_2116 | ||
| 912 | |a GBV_ILN_2118 | ||
| 912 | |a GBV_ILN_2119 | ||
| 912 | |a GBV_ILN_2122 | ||
| 912 | |a GBV_ILN_2129 | ||
| 912 | |a GBV_ILN_2143 | ||
| 912 | |a GBV_ILN_2144 | ||
| 912 | |a GBV_ILN_2147 | ||
| 912 | |a GBV_ILN_2148 | ||
| 912 | |a GBV_ILN_2152 | ||
| 912 | |a GBV_ILN_2153 | ||
| 912 | |a GBV_ILN_2188 | ||
| 912 | |a GBV_ILN_2190 | ||
| 912 | |a GBV_ILN_2232 | ||
| 912 | |a GBV_ILN_2336 | ||
| 912 | |a GBV_ILN_2446 | ||
| 912 | |a GBV_ILN_2470 | ||
| 912 | |a GBV_ILN_2472 | ||
| 912 | |a GBV_ILN_2507 | ||
| 912 | |a GBV_ILN_2522 | ||
| 912 | |a GBV_ILN_2548 | ||
| 912 | |a GBV_ILN_4035 | ||
| 912 | |a GBV_ILN_4037 | ||
| 912 | |a GBV_ILN_4046 | ||
| 912 | |a GBV_ILN_4112 | ||
| 912 | |a GBV_ILN_4125 | ||
| 912 | |a GBV_ILN_4242 | ||
| 912 | |a GBV_ILN_4246 | ||
| 912 | |a GBV_ILN_4249 | ||
| 912 | |a GBV_ILN_4251 | ||
| 912 | |a GBV_ILN_4305 | ||
| 912 | |a GBV_ILN_4306 | ||
| 912 | |a GBV_ILN_4307 | ||
| 912 | |a GBV_ILN_4313 | ||
| 912 | |a GBV_ILN_4322 | ||
| 912 | |a GBV_ILN_4323 | ||
| 912 | |a GBV_ILN_4324 | ||
| 912 | |a GBV_ILN_4325 | ||
| 912 | |a GBV_ILN_4326 | ||
| 912 | |a GBV_ILN_4328 | ||
| 912 | |a GBV_ILN_4333 | ||
| 912 | |a GBV_ILN_4334 | ||
| 912 | |a GBV_ILN_4335 | ||
| 912 | |a GBV_ILN_4336 | ||
| 912 | |a GBV_ILN_4338 | ||
| 912 | |a GBV_ILN_4393 | ||
| 912 | |a GBV_ILN_4700 | ||
| 951 | |a AR | ||
| 952 | |d 29 |j 2018 |e 1 |b 24 |c 04 |h 717-732 | ||
| author_variant |
d g dg m m mm d p dp |
|---|---|
| matchkey_str |
article:1559002X:2018----::hmnmlouefipiecnann |
| hierarchy_sort_str |
2018 |
| publishDate |
2018 |
| allfields |
10.1007/s12220-018-0016-4 doi (DE-627)SPR025411764 (SPR)s12220-018-0016-4-e DE-627 ger DE-627 rakwb eng Galicer, Daniel verfasserin aut The Minimal Volume of Simplices Containing a Convex Body 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Mathematica Josephina, Inc. 2018 Abstract Let %$K \subset {\mathbb {R}}^n%$ be a convex body with barycenter at the origin. We show there is a simplex %$S \subset K%$ having also barycenter at the origin such that %$(\frac{\text {vol}(S)}{\text {vol}(K)})^{1/n} \ge \frac{c}{\sqrt{n}},%$ where %$c>0%$ is an absolute constant. This is achieved using stochastic geometric techniques. Precisely, if K is in isotropic position, we present a method to find centered simplices verifying the above bound that works with extremely high probability. By duality, given a convex body %$K \subset {\mathbb {R}}^n%$ we show there is a simplex S enclosing Kwith the same barycenter such that vol(S)vol(K)1/n≤dn,%$\begin{aligned} \left( \frac{\text {vol}(S)}{\text {vol}(K)}\right) ^{1/n} \le d \sqrt{n}, \end{aligned}%$for some absolute constant %$d>0%$. Up to the constant, the estimate cannot be lessened. Volume ratio (dpeaa)DE-He213 Simplices (dpeaa)DE-He213 Convex bodies (dpeaa)DE-He213 Isotropic position (dpeaa)DE-He213 Random simplices (dpeaa)DE-He213 Merzbacher, Mariano aut Pinasco, Damián aut Enthalten in The journal of geometric analysis New York, NY : Springer, 1991 29(2018), 1 vom: 24. Apr., Seite 717-732 (DE-627)496971867 (DE-600)2199635-0 1559-002X nnns volume:29 year:2018 number:1 day:24 month:04 pages:717-732 https://dx.doi.org/10.1007/s12220-018-0016-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 29 2018 1 24 04 717-732 |
| spelling |
10.1007/s12220-018-0016-4 doi (DE-627)SPR025411764 (SPR)s12220-018-0016-4-e DE-627 ger DE-627 rakwb eng Galicer, Daniel verfasserin aut The Minimal Volume of Simplices Containing a Convex Body 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Mathematica Josephina, Inc. 2018 Abstract Let %$K \subset {\mathbb {R}}^n%$ be a convex body with barycenter at the origin. We show there is a simplex %$S \subset K%$ having also barycenter at the origin such that %$(\frac{\text {vol}(S)}{\text {vol}(K)})^{1/n} \ge \frac{c}{\sqrt{n}},%$ where %$c>0%$ is an absolute constant. This is achieved using stochastic geometric techniques. Precisely, if K is in isotropic position, we present a method to find centered simplices verifying the above bound that works with extremely high probability. By duality, given a convex body %$K \subset {\mathbb {R}}^n%$ we show there is a simplex S enclosing Kwith the same barycenter such that vol(S)vol(K)1/n≤dn,%$\begin{aligned} \left( \frac{\text {vol}(S)}{\text {vol}(K)}\right) ^{1/n} \le d \sqrt{n}, \end{aligned}%$for some absolute constant %$d>0%$. Up to the constant, the estimate cannot be lessened. Volume ratio (dpeaa)DE-He213 Simplices (dpeaa)DE-He213 Convex bodies (dpeaa)DE-He213 Isotropic position (dpeaa)DE-He213 Random simplices (dpeaa)DE-He213 Merzbacher, Mariano aut Pinasco, Damián aut Enthalten in The journal of geometric analysis New York, NY : Springer, 1991 29(2018), 1 vom: 24. Apr., Seite 717-732 (DE-627)496971867 (DE-600)2199635-0 1559-002X nnns volume:29 year:2018 number:1 day:24 month:04 pages:717-732 https://dx.doi.org/10.1007/s12220-018-0016-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 29 2018 1 24 04 717-732 |
| allfields_unstemmed |
10.1007/s12220-018-0016-4 doi (DE-627)SPR025411764 (SPR)s12220-018-0016-4-e DE-627 ger DE-627 rakwb eng Galicer, Daniel verfasserin aut The Minimal Volume of Simplices Containing a Convex Body 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Mathematica Josephina, Inc. 2018 Abstract Let %$K \subset {\mathbb {R}}^n%$ be a convex body with barycenter at the origin. We show there is a simplex %$S \subset K%$ having also barycenter at the origin such that %$(\frac{\text {vol}(S)}{\text {vol}(K)})^{1/n} \ge \frac{c}{\sqrt{n}},%$ where %$c>0%$ is an absolute constant. This is achieved using stochastic geometric techniques. Precisely, if K is in isotropic position, we present a method to find centered simplices verifying the above bound that works with extremely high probability. By duality, given a convex body %$K \subset {\mathbb {R}}^n%$ we show there is a simplex S enclosing Kwith the same barycenter such that vol(S)vol(K)1/n≤dn,%$\begin{aligned} \left( \frac{\text {vol}(S)}{\text {vol}(K)}\right) ^{1/n} \le d \sqrt{n}, \end{aligned}%$for some absolute constant %$d>0%$. Up to the constant, the estimate cannot be lessened. Volume ratio (dpeaa)DE-He213 Simplices (dpeaa)DE-He213 Convex bodies (dpeaa)DE-He213 Isotropic position (dpeaa)DE-He213 Random simplices (dpeaa)DE-He213 Merzbacher, Mariano aut Pinasco, Damián aut Enthalten in The journal of geometric analysis New York, NY : Springer, 1991 29(2018), 1 vom: 24. Apr., Seite 717-732 (DE-627)496971867 (DE-600)2199635-0 1559-002X nnns volume:29 year:2018 number:1 day:24 month:04 pages:717-732 https://dx.doi.org/10.1007/s12220-018-0016-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 29 2018 1 24 04 717-732 |
| allfieldsGer |
10.1007/s12220-018-0016-4 doi (DE-627)SPR025411764 (SPR)s12220-018-0016-4-e DE-627 ger DE-627 rakwb eng Galicer, Daniel verfasserin aut The Minimal Volume of Simplices Containing a Convex Body 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Mathematica Josephina, Inc. 2018 Abstract Let %$K \subset {\mathbb {R}}^n%$ be a convex body with barycenter at the origin. We show there is a simplex %$S \subset K%$ having also barycenter at the origin such that %$(\frac{\text {vol}(S)}{\text {vol}(K)})^{1/n} \ge \frac{c}{\sqrt{n}},%$ where %$c>0%$ is an absolute constant. This is achieved using stochastic geometric techniques. Precisely, if K is in isotropic position, we present a method to find centered simplices verifying the above bound that works with extremely high probability. By duality, given a convex body %$K \subset {\mathbb {R}}^n%$ we show there is a simplex S enclosing Kwith the same barycenter such that vol(S)vol(K)1/n≤dn,%$\begin{aligned} \left( \frac{\text {vol}(S)}{\text {vol}(K)}\right) ^{1/n} \le d \sqrt{n}, \end{aligned}%$for some absolute constant %$d>0%$. Up to the constant, the estimate cannot be lessened. Volume ratio (dpeaa)DE-He213 Simplices (dpeaa)DE-He213 Convex bodies (dpeaa)DE-He213 Isotropic position (dpeaa)DE-He213 Random simplices (dpeaa)DE-He213 Merzbacher, Mariano aut Pinasco, Damián aut Enthalten in The journal of geometric analysis New York, NY : Springer, 1991 29(2018), 1 vom: 24. Apr., Seite 717-732 (DE-627)496971867 (DE-600)2199635-0 1559-002X nnns volume:29 year:2018 number:1 day:24 month:04 pages:717-732 https://dx.doi.org/10.1007/s12220-018-0016-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 29 2018 1 24 04 717-732 |
| allfieldsSound |
10.1007/s12220-018-0016-4 doi (DE-627)SPR025411764 (SPR)s12220-018-0016-4-e DE-627 ger DE-627 rakwb eng Galicer, Daniel verfasserin aut The Minimal Volume of Simplices Containing a Convex Body 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Mathematica Josephina, Inc. 2018 Abstract Let %$K \subset {\mathbb {R}}^n%$ be a convex body with barycenter at the origin. We show there is a simplex %$S \subset K%$ having also barycenter at the origin such that %$(\frac{\text {vol}(S)}{\text {vol}(K)})^{1/n} \ge \frac{c}{\sqrt{n}},%$ where %$c>0%$ is an absolute constant. This is achieved using stochastic geometric techniques. Precisely, if K is in isotropic position, we present a method to find centered simplices verifying the above bound that works with extremely high probability. By duality, given a convex body %$K \subset {\mathbb {R}}^n%$ we show there is a simplex S enclosing Kwith the same barycenter such that vol(S)vol(K)1/n≤dn,%$\begin{aligned} \left( \frac{\text {vol}(S)}{\text {vol}(K)}\right) ^{1/n} \le d \sqrt{n}, \end{aligned}%$for some absolute constant %$d>0%$. Up to the constant, the estimate cannot be lessened. Volume ratio (dpeaa)DE-He213 Simplices (dpeaa)DE-He213 Convex bodies (dpeaa)DE-He213 Isotropic position (dpeaa)DE-He213 Random simplices (dpeaa)DE-He213 Merzbacher, Mariano aut Pinasco, Damián aut Enthalten in The journal of geometric analysis New York, NY : Springer, 1991 29(2018), 1 vom: 24. Apr., Seite 717-732 (DE-627)496971867 (DE-600)2199635-0 1559-002X nnns volume:29 year:2018 number:1 day:24 month:04 pages:717-732 https://dx.doi.org/10.1007/s12220-018-0016-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 29 2018 1 24 04 717-732 |
| language |
English |
| source |
Enthalten in The journal of geometric analysis 29(2018), 1 vom: 24. Apr., Seite 717-732 volume:29 year:2018 number:1 day:24 month:04 pages:717-732 |
| sourceStr |
Enthalten in The journal of geometric analysis 29(2018), 1 vom: 24. Apr., Seite 717-732 volume:29 year:2018 number:1 day:24 month:04 pages:717-732 |
| format_phy_str_mv |
Article |
| institution |
findex.gbv.de |
| topic_facet |
Volume ratio Simplices Convex bodies Isotropic position Random simplices |
| isfreeaccess_bool |
false |
| container_title |
The journal of geometric analysis |
| authorswithroles_txt_mv |
Galicer, Daniel @@aut@@ Merzbacher, Mariano @@aut@@ Pinasco, Damián @@aut@@ |
| publishDateDaySort_date |
2018-04-24T00:00:00Z |
| hierarchy_top_id |
496971867 |
| id |
SPR025411764 |
| language_de |
englisch |
| fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR025411764</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230403070429.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201007s2018 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s12220-018-0016-4</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR025411764</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s12220-018-0016-4-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Galicer, Daniel</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="4"><subfield code="a">The Minimal Volume of Simplices Containing a Convex Body</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2018</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Mathematica Josephina, Inc. 2018</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Let %$K \subset {\mathbb {R}}^n%$ be a convex body with barycenter at the origin. We show there is a simplex %$S \subset K%$ having also barycenter at the origin such that %$(\frac{\text {vol}(S)}{\text {vol}(K)})^{1/n} \ge \frac{c}{\sqrt{n}},%$ where %$c>0%$ is an absolute constant. This is achieved using stochastic geometric techniques. Precisely, if K is in isotropic position, we present a method to find centered simplices verifying the above bound that works with extremely high probability. By duality, given a convex body %$K \subset {\mathbb {R}}^n%$ we show there is a simplex S enclosing Kwith the same barycenter such that vol(S)vol(K)1/n≤dn,%$\begin{aligned} \left( \frac{\text {vol}(S)}{\text {vol}(K)}\right) ^{1/n} \le d \sqrt{n}, \end{aligned}%$for some absolute constant %$d>0%$. Up to the constant, the estimate cannot be lessened.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Volume ratio</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Simplices</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Convex bodies</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Isotropic position</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Random simplices</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Merzbacher, Mariano</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Pinasco, Damián</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">The journal of geometric analysis</subfield><subfield code="d">New York, NY : Springer, 1991</subfield><subfield code="g">29(2018), 1 vom: 24. Apr., Seite 717-732</subfield><subfield code="w">(DE-627)496971867</subfield><subfield code="w">(DE-600)2199635-0</subfield><subfield code="x">1559-002X</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:29</subfield><subfield code="g">year:2018</subfield><subfield code="g">number:1</subfield><subfield code="g">day:24</subfield><subfield code="g">month:04</subfield><subfield code="g">pages:717-732</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://dx.doi.org/10.1007/s12220-018-0016-4</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_SPRINGER</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_11</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_20</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_22</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_23</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_24</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_31</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_32</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_39</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_40</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_60</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_62</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_63</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_65</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_69</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_73</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_74</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_90</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_95</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_100</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_105</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_110</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_120</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_138</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_150</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_151</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_152</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_161</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_170</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_171</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_187</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_213</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_224</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_230</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_250</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_281</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_285</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_293</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_370</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_602</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_636</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_702</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2001</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2003</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2004</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2005</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2006</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2007</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2008</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2009</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2010</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2011</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2014</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2015</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2020</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2021</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2025</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2026</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2027</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2031</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2034</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2037</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2038</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2039</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2044</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2048</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2049</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2050</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2055</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2057</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2059</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2061</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2064</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2065</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2068</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2070</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2086</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2088</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2093</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2106</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2107</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2108</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2110</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2111</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2112</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2113</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2116</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2118</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2119</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2122</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2129</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2143</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2144</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2147</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2148</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2152</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2153</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2188</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2190</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2232</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2336</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2446</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2470</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2472</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2507</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2522</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2548</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4035</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4037</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4046</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4112</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4125</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4242</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4246</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4249</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4251</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4305</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4306</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4307</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4313</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4322</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4323</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4324</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4325</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4326</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4328</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4333</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4334</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4335</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4336</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4338</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4393</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4700</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">29</subfield><subfield code="j">2018</subfield><subfield code="e">1</subfield><subfield code="b">24</subfield><subfield code="c">04</subfield><subfield code="h">717-732</subfield></datafield></record></collection>
|
| author |
Galicer, Daniel |
| spellingShingle |
Galicer, Daniel misc Volume ratio misc Simplices misc Convex bodies misc Isotropic position misc Random simplices The Minimal Volume of Simplices Containing a Convex Body |
| authorStr |
Galicer, Daniel |
| ppnlink_with_tag_str_mv |
@@773@@(DE-627)496971867 |
| format |
electronic Article |
| delete_txt_mv |
keep |
| author_role |
aut aut aut |
| collection |
springer |
| remote_str |
true |
| illustrated |
Not Illustrated |
| issn |
1559-002X |
| topic_title |
The Minimal Volume of Simplices Containing a Convex Body Volume ratio (dpeaa)DE-He213 Simplices (dpeaa)DE-He213 Convex bodies (dpeaa)DE-He213 Isotropic position (dpeaa)DE-He213 Random simplices (dpeaa)DE-He213 |
| topic |
misc Volume ratio misc Simplices misc Convex bodies misc Isotropic position misc Random simplices |
| topic_unstemmed |
misc Volume ratio misc Simplices misc Convex bodies misc Isotropic position misc Random simplices |
| topic_browse |
misc Volume ratio misc Simplices misc Convex bodies misc Isotropic position misc Random simplices |
| format_facet |
Elektronische Aufsätze Aufsätze Elektronische Ressource |
| format_main_str_mv |
Text Zeitschrift/Artikel |
| carriertype_str_mv |
cr |
| hierarchy_parent_title |
The journal of geometric analysis |
| hierarchy_parent_id |
496971867 |
| hierarchy_top_title |
The journal of geometric analysis |
| isfreeaccess_txt |
false |
| familylinks_str_mv |
(DE-627)496971867 (DE-600)2199635-0 |
| title |
The Minimal Volume of Simplices Containing a Convex Body |
| ctrlnum |
(DE-627)SPR025411764 (SPR)s12220-018-0016-4-e |
| title_full |
The Minimal Volume of Simplices Containing a Convex Body |
| author_sort |
Galicer, Daniel |
| journal |
The journal of geometric analysis |
| journalStr |
The journal of geometric analysis |
| lang_code |
eng |
| isOA_bool |
false |
| recordtype |
marc |
| publishDateSort |
2018 |
| contenttype_str_mv |
txt |
| container_start_page |
717 |
| author_browse |
Galicer, Daniel Merzbacher, Mariano Pinasco, Damián |
| container_volume |
29 |
| format_se |
Elektronische Aufsätze |
| author-letter |
Galicer, Daniel |
| doi_str_mv |
10.1007/s12220-018-0016-4 |
| title_sort |
minimal volume of simplices containing a convex body |
| title_auth |
The Minimal Volume of Simplices Containing a Convex Body |
| abstract |
Abstract Let %$K \subset {\mathbb {R}}^n%$ be a convex body with barycenter at the origin. We show there is a simplex %$S \subset K%$ having also barycenter at the origin such that %$(\frac{\text {vol}(S)}{\text {vol}(K)})^{1/n} \ge \frac{c}{\sqrt{n}},%$ where %$c>0%$ is an absolute constant. This is achieved using stochastic geometric techniques. Precisely, if K is in isotropic position, we present a method to find centered simplices verifying the above bound that works with extremely high probability. By duality, given a convex body %$K \subset {\mathbb {R}}^n%$ we show there is a simplex S enclosing Kwith the same barycenter such that vol(S)vol(K)1/n≤dn,%$\begin{aligned} \left( \frac{\text {vol}(S)}{\text {vol}(K)}\right) ^{1/n} \le d \sqrt{n}, \end{aligned}%$for some absolute constant %$d>0%$. Up to the constant, the estimate cannot be lessened. © Mathematica Josephina, Inc. 2018 |
| abstractGer |
Abstract Let %$K \subset {\mathbb {R}}^n%$ be a convex body with barycenter at the origin. We show there is a simplex %$S \subset K%$ having also barycenter at the origin such that %$(\frac{\text {vol}(S)}{\text {vol}(K)})^{1/n} \ge \frac{c}{\sqrt{n}},%$ where %$c>0%$ is an absolute constant. This is achieved using stochastic geometric techniques. Precisely, if K is in isotropic position, we present a method to find centered simplices verifying the above bound that works with extremely high probability. By duality, given a convex body %$K \subset {\mathbb {R}}^n%$ we show there is a simplex S enclosing Kwith the same barycenter such that vol(S)vol(K)1/n≤dn,%$\begin{aligned} \left( \frac{\text {vol}(S)}{\text {vol}(K)}\right) ^{1/n} \le d \sqrt{n}, \end{aligned}%$for some absolute constant %$d>0%$. Up to the constant, the estimate cannot be lessened. © Mathematica Josephina, Inc. 2018 |
| abstract_unstemmed |
Abstract Let %$K \subset {\mathbb {R}}^n%$ be a convex body with barycenter at the origin. We show there is a simplex %$S \subset K%$ having also barycenter at the origin such that %$(\frac{\text {vol}(S)}{\text {vol}(K)})^{1/n} \ge \frac{c}{\sqrt{n}},%$ where %$c>0%$ is an absolute constant. This is achieved using stochastic geometric techniques. Precisely, if K is in isotropic position, we present a method to find centered simplices verifying the above bound that works with extremely high probability. By duality, given a convex body %$K \subset {\mathbb {R}}^n%$ we show there is a simplex S enclosing Kwith the same barycenter such that vol(S)vol(K)1/n≤dn,%$\begin{aligned} \left( \frac{\text {vol}(S)}{\text {vol}(K)}\right) ^{1/n} \le d \sqrt{n}, \end{aligned}%$for some absolute constant %$d>0%$. Up to the constant, the estimate cannot be lessened. © Mathematica Josephina, Inc. 2018 |
| collection_details |
GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 |
| container_issue |
1 |
| title_short |
The Minimal Volume of Simplices Containing a Convex Body |
| url |
https://dx.doi.org/10.1007/s12220-018-0016-4 |
| remote_bool |
true |
| author2 |
Merzbacher, Mariano Pinasco, Damián |
| author2Str |
Merzbacher, Mariano Pinasco, Damián |
| ppnlink |
496971867 |
| mediatype_str_mv |
c |
| isOA_txt |
false |
| hochschulschrift_bool |
false |
| doi_str |
10.1007/s12220-018-0016-4 |
| up_date |
2024-07-03T15:50:19.737Z |
| _version_ |
1803573599666176000 |
| fullrecord_marcxml |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR025411764</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230403070429.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201007s2018 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s12220-018-0016-4</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR025411764</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s12220-018-0016-4-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Galicer, Daniel</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="4"><subfield code="a">The Minimal Volume of Simplices Containing a Convex Body</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2018</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Mathematica Josephina, Inc. 2018</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Let %$K \subset {\mathbb {R}}^n%$ be a convex body with barycenter at the origin. We show there is a simplex %$S \subset K%$ having also barycenter at the origin such that %$(\frac{\text {vol}(S)}{\text {vol}(K)})^{1/n} \ge \frac{c}{\sqrt{n}},%$ where %$c>0%$ is an absolute constant. This is achieved using stochastic geometric techniques. Precisely, if K is in isotropic position, we present a method to find centered simplices verifying the above bound that works with extremely high probability. By duality, given a convex body %$K \subset {\mathbb {R}}^n%$ we show there is a simplex S enclosing Kwith the same barycenter such that vol(S)vol(K)1/n≤dn,%$\begin{aligned} \left( \frac{\text {vol}(S)}{\text {vol}(K)}\right) ^{1/n} \le d \sqrt{n}, \end{aligned}%$for some absolute constant %$d>0%$. Up to the constant, the estimate cannot be lessened.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Volume ratio</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Simplices</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Convex bodies</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Isotropic position</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Random simplices</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Merzbacher, Mariano</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Pinasco, Damián</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">The journal of geometric analysis</subfield><subfield code="d">New York, NY : Springer, 1991</subfield><subfield code="g">29(2018), 1 vom: 24. Apr., Seite 717-732</subfield><subfield code="w">(DE-627)496971867</subfield><subfield code="w">(DE-600)2199635-0</subfield><subfield code="x">1559-002X</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:29</subfield><subfield code="g">year:2018</subfield><subfield code="g">number:1</subfield><subfield code="g">day:24</subfield><subfield code="g">month:04</subfield><subfield code="g">pages:717-732</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://dx.doi.org/10.1007/s12220-018-0016-4</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_SPRINGER</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_11</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_20</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_22</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_23</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_24</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_31</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_32</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_39</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_40</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_60</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_62</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_63</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_65</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_69</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_73</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_74</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_90</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_95</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_100</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_105</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_110</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_120</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_138</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_150</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_151</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_152</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_161</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_170</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_171</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_187</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_213</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_224</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_230</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_250</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_281</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_285</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_293</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_370</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_602</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_636</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_702</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2001</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2003</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2004</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2005</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2006</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2007</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2008</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2009</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2010</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2011</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2014</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2015</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2020</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2021</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2025</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2026</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2027</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2031</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2034</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2037</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2038</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2039</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2044</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2048</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2049</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2050</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2055</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2057</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2059</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2061</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2064</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2065</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2068</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2070</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2086</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2088</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2093</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2106</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2107</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2108</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2110</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2111</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2112</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2113</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2116</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2118</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2119</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2122</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2129</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2143</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2144</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2147</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2148</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2152</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2153</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2188</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2190</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2232</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2336</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2446</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2470</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2472</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2507</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2522</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2548</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4035</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4037</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4046</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4112</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4125</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4242</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4246</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4249</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4251</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4305</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4306</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4307</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4313</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4322</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4323</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4324</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4325</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4326</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4328</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4333</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4334</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4335</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4336</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4338</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4393</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4700</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">29</subfield><subfield code="j">2018</subfield><subfield code="e">1</subfield><subfield code="b">24</subfield><subfield code="c">04</subfield><subfield code="h">717-732</subfield></datafield></record></collection>
|
| score |
7.4014235 |