Higher-Dimensional Stick Percolation

Abstract We consider two cases of the so-called stick percolation model with sticks of length L. In the first case, the orientation is chosen independently and uniformly, while in the second all sticks are oriented along the same direction. We study their respective critical values %$\lambda _c(L)%$...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Broman, Erik I. [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2021

Schlagwörter:	Continuum-percolation Stick percolation Scaling exponent

Anmerkung:	© The Author(s) 2021

Übergeordnetes Werk:	Enthalten in: Journal of statistical physics - New York, NY [u.a.] : Springer Science + Business Media B.V., 1969, 186(2021), 1 vom: 07. Dez.
Übergeordnetes Werk:	volume:186 ; year:2021 ; number:1 ; day:07 ; month:12

Links:	Volltext

DOI / URN:	10.1007/s10955-021-02849-4

Katalog-ID:	SPR045754837

Internformat


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520			\|a Abstract We consider two cases of the so-called stick percolation model with sticks of length L. In the first case, the orientation is chosen independently and uniformly, while in the second all sticks are oriented along the same direction. We study their respective critical values %$\lambda _c(L)%$ of the percolation phase transition, and in particular we investigate the asymptotic behavior of %$\lambda _c(L)%$ as %$L\rightarrow \infty %$ for both of these cases. In the first case we prove that %$\lambda _c(L)\sim L^{-2}%$ for any %$d\ge 2,%$ while in the second we prove that %$\lambda _c(L)\sim L^{-1}%$ for any %$d\ge 2.%$
650		4	\|a Continuum-percolation \|7 (dpeaa)DE-He213
650		4	\|a Stick percolation \|7 (dpeaa)DE-He213
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matchkey_str	article:15729613:2021----::ihriesoasike
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publishDate	2021
allfields	10.1007/s10955-021-02849-4 doi (DE-627)SPR045754837 (SPR)s10955-021-02849-4-e DE-627 ger DE-627 rakwb eng Broman, Erik I. verfasserin (orcid)0000-0002-1751-2796 aut Higher-Dimensional Stick Percolation 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2021 Abstract We consider two cases of the so-called stick percolation model with sticks of length L. In the first case, the orientation is chosen independently and uniformly, while in the second all sticks are oriented along the same direction. We study their respective critical values %$\lambda _c(L)%$ of the percolation phase transition, and in particular we investigate the asymptotic behavior of %$\lambda _c(L)%$ as %$L\rightarrow \infty %$ for both of these cases. In the first case we prove that %$\lambda _c(L)\sim L^{-2}%$ for any %$d\ge 2,%$ while in the second we prove that %$\lambda _c(L)\sim L^{-1}%$ for any %$d\ge 2.%$ Continuum-percolation (dpeaa)DE-He213 Stick percolation (dpeaa)DE-He213 Scaling exponent (dpeaa)DE-He213 Enthalten in Journal of statistical physics New York, NY [u.a.] : Springer Science + Business Media B.V., 1969 186(2021), 1 vom: 07. Dez. (DE-627)320578437 (DE-600)2017302-7 1572-9613 nnns volume:186 year:2021 number:1 day:07 month:12 https://dx.doi.org/10.1007/s10955-021-02849-4 kostenfrei 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_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 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_206 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_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 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_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_4126 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 186 2021 1 07 12
spelling	10.1007/s10955-021-02849-4 doi (DE-627)SPR045754837 (SPR)s10955-021-02849-4-e DE-627 ger DE-627 rakwb eng Broman, Erik I. verfasserin (orcid)0000-0002-1751-2796 aut Higher-Dimensional Stick Percolation 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2021 Abstract We consider two cases of the so-called stick percolation model with sticks of length L. In the first case, the orientation is chosen independently and uniformly, while in the second all sticks are oriented along the same direction. We study their respective critical values %$\lambda _c(L)%$ of the percolation phase transition, and in particular we investigate the asymptotic behavior of %$\lambda _c(L)%$ as %$L\rightarrow \infty %$ for both of these cases. In the first case we prove that %$\lambda _c(L)\sim L^{-2}%$ for any %$d\ge 2,%$ while in the second we prove that %$\lambda _c(L)\sim L^{-1}%$ for any %$d\ge 2.%$ Continuum-percolation (dpeaa)DE-He213 Stick percolation (dpeaa)DE-He213 Scaling exponent (dpeaa)DE-He213 Enthalten in Journal of statistical physics New York, NY [u.a.] : Springer Science + Business Media B.V., 1969 186(2021), 1 vom: 07. Dez. (DE-627)320578437 (DE-600)2017302-7 1572-9613 nnns volume:186 year:2021 number:1 day:07 month:12 https://dx.doi.org/10.1007/s10955-021-02849-4 kostenfrei 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_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 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_206 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_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 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_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_4126 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 186 2021 1 07 12
allfields_unstemmed	10.1007/s10955-021-02849-4 doi (DE-627)SPR045754837 (SPR)s10955-021-02849-4-e DE-627 ger DE-627 rakwb eng Broman, Erik I. verfasserin (orcid)0000-0002-1751-2796 aut Higher-Dimensional Stick Percolation 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2021 Abstract We consider two cases of the so-called stick percolation model with sticks of length L. In the first case, the orientation is chosen independently and uniformly, while in the second all sticks are oriented along the same direction. We study their respective critical values %$\lambda _c(L)%$ of the percolation phase transition, and in particular we investigate the asymptotic behavior of %$\lambda _c(L)%$ as %$L\rightarrow \infty %$ for both of these cases. In the first case we prove that %$\lambda _c(L)\sim L^{-2}%$ for any %$d\ge 2,%$ while in the second we prove that %$\lambda _c(L)\sim L^{-1}%$ for any %$d\ge 2.%$ Continuum-percolation (dpeaa)DE-He213 Stick percolation (dpeaa)DE-He213 Scaling exponent (dpeaa)DE-He213 Enthalten in Journal of statistical physics New York, NY [u.a.] : Springer Science + Business Media B.V., 1969 186(2021), 1 vom: 07. Dez. (DE-627)320578437 (DE-600)2017302-7 1572-9613 nnns volume:186 year:2021 number:1 day:07 month:12 https://dx.doi.org/10.1007/s10955-021-02849-4 kostenfrei 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_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 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_206 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_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 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_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_4126 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 186 2021 1 07 12
allfieldsGer	10.1007/s10955-021-02849-4 doi (DE-627)SPR045754837 (SPR)s10955-021-02849-4-e DE-627 ger DE-627 rakwb eng Broman, Erik I. verfasserin (orcid)0000-0002-1751-2796 aut Higher-Dimensional Stick Percolation 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2021 Abstract We consider two cases of the so-called stick percolation model with sticks of length L. In the first case, the orientation is chosen independently and uniformly, while in the second all sticks are oriented along the same direction. We study their respective critical values %$\lambda _c(L)%$ of the percolation phase transition, and in particular we investigate the asymptotic behavior of %$\lambda _c(L)%$ as %$L\rightarrow \infty %$ for both of these cases. In the first case we prove that %$\lambda _c(L)\sim L^{-2}%$ for any %$d\ge 2,%$ while in the second we prove that %$\lambda _c(L)\sim L^{-1}%$ for any %$d\ge 2.%$ Continuum-percolation (dpeaa)DE-He213 Stick percolation (dpeaa)DE-He213 Scaling exponent (dpeaa)DE-He213 Enthalten in Journal of statistical physics New York, NY [u.a.] : Springer Science + Business Media B.V., 1969 186(2021), 1 vom: 07. Dez. (DE-627)320578437 (DE-600)2017302-7 1572-9613 nnns volume:186 year:2021 number:1 day:07 month:12 https://dx.doi.org/10.1007/s10955-021-02849-4 kostenfrei 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_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 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_206 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_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 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_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_4126 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 186 2021 1 07 12
allfieldsSound	10.1007/s10955-021-02849-4 doi (DE-627)SPR045754837 (SPR)s10955-021-02849-4-e DE-627 ger DE-627 rakwb eng Broman, Erik I. verfasserin (orcid)0000-0002-1751-2796 aut Higher-Dimensional Stick Percolation 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2021 Abstract We consider two cases of the so-called stick percolation model with sticks of length L. In the first case, the orientation is chosen independently and uniformly, while in the second all sticks are oriented along the same direction. We study their respective critical values %$\lambda _c(L)%$ of the percolation phase transition, and in particular we investigate the asymptotic behavior of %$\lambda _c(L)%$ as %$L\rightarrow \infty %$ for both of these cases. In the first case we prove that %$\lambda _c(L)\sim L^{-2}%$ for any %$d\ge 2,%$ while in the second we prove that %$\lambda _c(L)\sim L^{-1}%$ for any %$d\ge 2.%$ Continuum-percolation (dpeaa)DE-He213 Stick percolation (dpeaa)DE-He213 Scaling exponent (dpeaa)DE-He213 Enthalten in Journal of statistical physics New York, NY [u.a.] : Springer Science + Business Media B.V., 1969 186(2021), 1 vom: 07. Dez. (DE-627)320578437 (DE-600)2017302-7 1572-9613 nnns volume:186 year:2021 number:1 day:07 month:12 https://dx.doi.org/10.1007/s10955-021-02849-4 kostenfrei 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_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 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_206 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_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 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_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_4126 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 186 2021 1 07 12
language	English
source	Enthalten in Journal of statistical physics 186(2021), 1 vom: 07. Dez. volume:186 year:2021 number:1 day:07 month:12
sourceStr	Enthalten in Journal of statistical physics 186(2021), 1 vom: 07. Dez. volume:186 year:2021 number:1 day:07 month:12
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Continuum-percolation Stick percolation Scaling exponent
isfreeaccess_bool	true
container_title	Journal of statistical physics
authorswithroles_txt_mv	Broman, Erik I. @@aut@@
publishDateDaySort_date	2021-12-07T00:00:00Z
hierarchy_top_id	320578437
id	SPR045754837
language_de	englisch
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author	Broman, Erik I.
spellingShingle	Broman, Erik I. misc Continuum-percolation misc Stick percolation misc Scaling exponent Higher-Dimensional Stick Percolation
authorStr	Broman, Erik I.
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topic_title	Higher-Dimensional Stick Percolation Continuum-percolation (dpeaa)DE-He213 Stick percolation (dpeaa)DE-He213 Scaling exponent (dpeaa)DE-He213
topic	misc Continuum-percolation misc Stick percolation misc Scaling exponent
topic_unstemmed	misc Continuum-percolation misc Stick percolation misc Scaling exponent
topic_browse	misc Continuum-percolation misc Stick percolation misc Scaling exponent
format_facet	Elektronische Aufsätze Aufsätze Elektronische Ressource
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title	Higher-Dimensional Stick Percolation
ctrlnum	(DE-627)SPR045754837 (SPR)s10955-021-02849-4-e
title_full	Higher-Dimensional Stick Percolation
author_sort	Broman, Erik I.
journal	Journal of statistical physics
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author_browse	Broman, Erik I.
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format_se	Elektronische Aufsätze
author-letter	Broman, Erik I.
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title_sort	higher-dimensional stick percolation
title_auth	Higher-Dimensional Stick Percolation
abstract	Abstract We consider two cases of the so-called stick percolation model with sticks of length L. In the first case, the orientation is chosen independently and uniformly, while in the second all sticks are oriented along the same direction. We study their respective critical values %$\lambda _c(L)%$ of the percolation phase transition, and in particular we investigate the asymptotic behavior of %$\lambda _c(L)%$ as %$L\rightarrow \infty %$ for both of these cases. In the first case we prove that %$\lambda _c(L)\sim L^{-2}%$ for any %$d\ge 2,%$ while in the second we prove that %$\lambda _c(L)\sim L^{-1}%$ for any %$d\ge 2.%$ © The Author(s) 2021
abstractGer	Abstract We consider two cases of the so-called stick percolation model with sticks of length L. In the first case, the orientation is chosen independently and uniformly, while in the second all sticks are oriented along the same direction. We study their respective critical values %$\lambda _c(L)%$ of the percolation phase transition, and in particular we investigate the asymptotic behavior of %$\lambda _c(L)%$ as %$L\rightarrow \infty %$ for both of these cases. In the first case we prove that %$\lambda _c(L)\sim L^{-2}%$ for any %$d\ge 2,%$ while in the second we prove that %$\lambda _c(L)\sim L^{-1}%$ for any %$d\ge 2.%$ © The Author(s) 2021
abstract_unstemmed	Abstract We consider two cases of the so-called stick percolation model with sticks of length L. In the first case, the orientation is chosen independently and uniformly, while in the second all sticks are oriented along the same direction. We study their respective critical values %$\lambda _c(L)%$ of the percolation phase transition, and in particular we investigate the asymptotic behavior of %$\lambda _c(L)%$ as %$L\rightarrow \infty %$ for both of these cases. In the first case we prove that %$\lambda _c(L)\sim L^{-2}%$ for any %$d\ge 2,%$ while in the second we prove that %$\lambda _c(L)\sim L^{-1}%$ for any %$d\ge 2.%$ © The Author(s) 2021
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title_short	Higher-Dimensional Stick Percolation
url	https://dx.doi.org/10.1007/s10955-021-02849-4
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doi_str	10.1007/s10955-021-02849-4
up_date	2024-07-03T18:04:27.626Z
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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">SPR045754837</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230509101011.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">211208s2021 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s10955-021-02849-4</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR045754837</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s10955-021-02849-4-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">Broman, Erik I.</subfield><subfield code="e">verfasserin</subfield><subfield code="0">(orcid)0000-0002-1751-2796</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Higher-Dimensional Stick Percolation</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2021</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">© The Author(s) 2021</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract We consider two cases of the so-called stick percolation model with sticks of length L. In the first case, the orientation is chosen independently and uniformly, while in the second all sticks are oriented along the same direction. We study their respective critical values %$\lambda _c(L)%$ of the percolation phase transition, and in particular we investigate the asymptotic behavior of %$\lambda _c(L)%$ as %$L\rightarrow \infty %$ for both of these cases. In the first case we prove that %$\lambda _c(L)\sim L^{-2}%$ for any %$d\ge 2,%$ while in the second we prove that %$\lambda _c(L)\sim L^{-1}%$ for any %$d\ge 2.%$</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Continuum-percolation</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Stick percolation</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Scaling exponent</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Journal of statistical physics</subfield><subfield code="d">New York, NY [u.a.] : Springer Science + Business Media B.V., 1969</subfield><subfield code="g">186(2021), 1 vom: 07. 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