Functional limit theorems for random regular graphs
Abstract Consider %$d%$ uniformly random permutation matrices on %$n%$ labels. Consider the sum of these matrices along with their transposes. The total can be interpreted as the adjacency matrix of a random regular graph of degree %$2d%$ on %$n%$ vertices. We consider limit theorems for various com...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Dumitriu, Ioana [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2012 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag 2012 |
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| Übergeordnetes Werk: |
Enthalten in: Probability theory and related fields - Berlin : Springer, 1992, 156(2012), 3-4 vom: 25. Aug., Seite 921-975 |
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| Übergeordnetes Werk: |
volume:156 ; year:2012 ; number:3-4 ; day:25 ; month:08 ; pages:921-975 |
| Links: |
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| DOI / URN: |
10.1007/s00440-012-0447-y |
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| Katalog-ID: |
SPR006004547 |
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| 100 | 1 | |a Dumitriu, Ioana |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Functional limit theorems for random regular graphs |
| 264 | 1 | |c 2012 | |
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| 520 | |a Abstract Consider %$d%$ uniformly random permutation matrices on %$n%$ labels. Consider the sum of these matrices along with their transposes. The total can be interpreted as the adjacency matrix of a random regular graph of degree %$2d%$ on %$n%$ vertices. We consider limit theorems for various combinatorial and analytical properties of this graph (or the matrix) as %$n%$ grows to infinity, either when %$d%$ is kept fixed or grows slowly with %$n%$. In a suitable weak convergence framework, we prove that the (finite but growing in length) sequences of the number of short cycles and of cyclically non-backtracking walks converge to distributional limits. We estimate the total variation distance from the limit using Stein’s method. As an application of these results we derive limits of linear functionals of the eigenvalues of the adjacency matrix. A key step in this latter derivation is an extension of the Kahn–Szemerédi argument for estimating the second largest eigenvalue for all values of %$d%$ and %$n%$. | ||
| 650 | 4 | |a Random regular graphs |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Sparse random matrices |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Poisson approximation |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Linear eigenvalue statistics |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Infinitely divisible distributions |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Johnson, Tobias |4 aut | |
| 700 | 1 | |a Pal, Soumik |4 aut | |
| 700 | 1 | |a Paquette, Elliot |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Probability theory and related fields |d Berlin : Springer, 1992 |g 156(2012), 3-4 vom: 25. Aug., Seite 921-975 |w (DE-627)254638791 |w (DE-600)1462994-X |x 1432-2064 |7 nnns |
| 773 | 1 | 8 | |g volume:156 |g year:2012 |g number:3-4 |g day:25 |g month:08 |g pages:921-975 |
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10.1007/s00440-012-0447-y doi (DE-627)SPR006004547 (SPR)s00440-012-0447-y-e DE-627 ger DE-627 rakwb eng Dumitriu, Ioana verfasserin aut Functional limit theorems for random regular graphs 2012 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2012 Abstract Consider %$d%$ uniformly random permutation matrices on %$n%$ labels. Consider the sum of these matrices along with their transposes. The total can be interpreted as the adjacency matrix of a random regular graph of degree %$2d%$ on %$n%$ vertices. We consider limit theorems for various combinatorial and analytical properties of this graph (or the matrix) as %$n%$ grows to infinity, either when %$d%$ is kept fixed or grows slowly with %$n%$. In a suitable weak convergence framework, we prove that the (finite but growing in length) sequences of the number of short cycles and of cyclically non-backtracking walks converge to distributional limits. We estimate the total variation distance from the limit using Stein’s method. As an application of these results we derive limits of linear functionals of the eigenvalues of the adjacency matrix. A key step in this latter derivation is an extension of the Kahn–Szemerédi argument for estimating the second largest eigenvalue for all values of %$d%$ and %$n%$. Random regular graphs (dpeaa)DE-He213 Sparse random matrices (dpeaa)DE-He213 Poisson approximation (dpeaa)DE-He213 Linear eigenvalue statistics (dpeaa)DE-He213 Infinitely divisible distributions (dpeaa)DE-He213 Johnson, Tobias aut Pal, Soumik aut Paquette, Elliot aut Enthalten in Probability theory and related fields Berlin : Springer, 1992 156(2012), 3-4 vom: 25. Aug., Seite 921-975 (DE-627)254638791 (DE-600)1462994-X 1432-2064 nnns volume:156 year:2012 number:3-4 day:25 month:08 pages:921-975 https://dx.doi.org/10.1007/s00440-012-0447-y 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_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_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 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_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_4012 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 156 2012 3-4 25 08 921-975 |
| spelling |
10.1007/s00440-012-0447-y doi (DE-627)SPR006004547 (SPR)s00440-012-0447-y-e DE-627 ger DE-627 rakwb eng Dumitriu, Ioana verfasserin aut Functional limit theorems for random regular graphs 2012 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2012 Abstract Consider %$d%$ uniformly random permutation matrices on %$n%$ labels. Consider the sum of these matrices along with their transposes. The total can be interpreted as the adjacency matrix of a random regular graph of degree %$2d%$ on %$n%$ vertices. We consider limit theorems for various combinatorial and analytical properties of this graph (or the matrix) as %$n%$ grows to infinity, either when %$d%$ is kept fixed or grows slowly with %$n%$. In a suitable weak convergence framework, we prove that the (finite but growing in length) sequences of the number of short cycles and of cyclically non-backtracking walks converge to distributional limits. We estimate the total variation distance from the limit using Stein’s method. As an application of these results we derive limits of linear functionals of the eigenvalues of the adjacency matrix. A key step in this latter derivation is an extension of the Kahn–Szemerédi argument for estimating the second largest eigenvalue for all values of %$d%$ and %$n%$. Random regular graphs (dpeaa)DE-He213 Sparse random matrices (dpeaa)DE-He213 Poisson approximation (dpeaa)DE-He213 Linear eigenvalue statistics (dpeaa)DE-He213 Infinitely divisible distributions (dpeaa)DE-He213 Johnson, Tobias aut Pal, Soumik aut Paquette, Elliot aut Enthalten in Probability theory and related fields Berlin : Springer, 1992 156(2012), 3-4 vom: 25. Aug., Seite 921-975 (DE-627)254638791 (DE-600)1462994-X 1432-2064 nnns volume:156 year:2012 number:3-4 day:25 month:08 pages:921-975 https://dx.doi.org/10.1007/s00440-012-0447-y 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_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_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 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_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_4012 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 156 2012 3-4 25 08 921-975 |
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10.1007/s00440-012-0447-y doi (DE-627)SPR006004547 (SPR)s00440-012-0447-y-e DE-627 ger DE-627 rakwb eng Dumitriu, Ioana verfasserin aut Functional limit theorems for random regular graphs 2012 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2012 Abstract Consider %$d%$ uniformly random permutation matrices on %$n%$ labels. Consider the sum of these matrices along with their transposes. The total can be interpreted as the adjacency matrix of a random regular graph of degree %$2d%$ on %$n%$ vertices. We consider limit theorems for various combinatorial and analytical properties of this graph (or the matrix) as %$n%$ grows to infinity, either when %$d%$ is kept fixed or grows slowly with %$n%$. In a suitable weak convergence framework, we prove that the (finite but growing in length) sequences of the number of short cycles and of cyclically non-backtracking walks converge to distributional limits. We estimate the total variation distance from the limit using Stein’s method. As an application of these results we derive limits of linear functionals of the eigenvalues of the adjacency matrix. A key step in this latter derivation is an extension of the Kahn–Szemerédi argument for estimating the second largest eigenvalue for all values of %$d%$ and %$n%$. Random regular graphs (dpeaa)DE-He213 Sparse random matrices (dpeaa)DE-He213 Poisson approximation (dpeaa)DE-He213 Linear eigenvalue statistics (dpeaa)DE-He213 Infinitely divisible distributions (dpeaa)DE-He213 Johnson, Tobias aut Pal, Soumik aut Paquette, Elliot aut Enthalten in Probability theory and related fields Berlin : Springer, 1992 156(2012), 3-4 vom: 25. Aug., Seite 921-975 (DE-627)254638791 (DE-600)1462994-X 1432-2064 nnns volume:156 year:2012 number:3-4 day:25 month:08 pages:921-975 https://dx.doi.org/10.1007/s00440-012-0447-y 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_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_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 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_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_4012 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 156 2012 3-4 25 08 921-975 |
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10.1007/s00440-012-0447-y doi (DE-627)SPR006004547 (SPR)s00440-012-0447-y-e DE-627 ger DE-627 rakwb eng Dumitriu, Ioana verfasserin aut Functional limit theorems for random regular graphs 2012 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2012 Abstract Consider %$d%$ uniformly random permutation matrices on %$n%$ labels. Consider the sum of these matrices along with their transposes. The total can be interpreted as the adjacency matrix of a random regular graph of degree %$2d%$ on %$n%$ vertices. We consider limit theorems for various combinatorial and analytical properties of this graph (or the matrix) as %$n%$ grows to infinity, either when %$d%$ is kept fixed or grows slowly with %$n%$. In a suitable weak convergence framework, we prove that the (finite but growing in length) sequences of the number of short cycles and of cyclically non-backtracking walks converge to distributional limits. We estimate the total variation distance from the limit using Stein’s method. As an application of these results we derive limits of linear functionals of the eigenvalues of the adjacency matrix. A key step in this latter derivation is an extension of the Kahn–Szemerédi argument for estimating the second largest eigenvalue for all values of %$d%$ and %$n%$. Random regular graphs (dpeaa)DE-He213 Sparse random matrices (dpeaa)DE-He213 Poisson approximation (dpeaa)DE-He213 Linear eigenvalue statistics (dpeaa)DE-He213 Infinitely divisible distributions (dpeaa)DE-He213 Johnson, Tobias aut Pal, Soumik aut Paquette, Elliot aut Enthalten in Probability theory and related fields Berlin : Springer, 1992 156(2012), 3-4 vom: 25. Aug., Seite 921-975 (DE-627)254638791 (DE-600)1462994-X 1432-2064 nnns volume:156 year:2012 number:3-4 day:25 month:08 pages:921-975 https://dx.doi.org/10.1007/s00440-012-0447-y 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_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_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 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_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_4012 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 156 2012 3-4 25 08 921-975 |
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10.1007/s00440-012-0447-y doi (DE-627)SPR006004547 (SPR)s00440-012-0447-y-e DE-627 ger DE-627 rakwb eng Dumitriu, Ioana verfasserin aut Functional limit theorems for random regular graphs 2012 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2012 Abstract Consider %$d%$ uniformly random permutation matrices on %$n%$ labels. Consider the sum of these matrices along with their transposes. The total can be interpreted as the adjacency matrix of a random regular graph of degree %$2d%$ on %$n%$ vertices. We consider limit theorems for various combinatorial and analytical properties of this graph (or the matrix) as %$n%$ grows to infinity, either when %$d%$ is kept fixed or grows slowly with %$n%$. In a suitable weak convergence framework, we prove that the (finite but growing in length) sequences of the number of short cycles and of cyclically non-backtracking walks converge to distributional limits. We estimate the total variation distance from the limit using Stein’s method. As an application of these results we derive limits of linear functionals of the eigenvalues of the adjacency matrix. A key step in this latter derivation is an extension of the Kahn–Szemerédi argument for estimating the second largest eigenvalue for all values of %$d%$ and %$n%$. Random regular graphs (dpeaa)DE-He213 Sparse random matrices (dpeaa)DE-He213 Poisson approximation (dpeaa)DE-He213 Linear eigenvalue statistics (dpeaa)DE-He213 Infinitely divisible distributions (dpeaa)DE-He213 Johnson, Tobias aut Pal, Soumik aut Paquette, Elliot aut Enthalten in Probability theory and related fields Berlin : Springer, 1992 156(2012), 3-4 vom: 25. Aug., Seite 921-975 (DE-627)254638791 (DE-600)1462994-X 1432-2064 nnns volume:156 year:2012 number:3-4 day:25 month:08 pages:921-975 https://dx.doi.org/10.1007/s00440-012-0447-y 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_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_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 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_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_4012 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 156 2012 3-4 25 08 921-975 |
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Enthalten in Probability theory and related fields 156(2012), 3-4 vom: 25. Aug., Seite 921-975 volume:156 year:2012 number:3-4 day:25 month:08 pages:921-975 |
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Dumitriu, Ioana @@aut@@ Johnson, Tobias @@aut@@ Pal, Soumik @@aut@@ Paquette, Elliot @@aut@@ |
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Dumitriu, Ioana |
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Dumitriu, Ioana misc Random regular graphs misc Sparse random matrices misc Poisson approximation misc Linear eigenvalue statistics misc Infinitely divisible distributions Functional limit theorems for random regular graphs |
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Functional limit theorems for random regular graphs Random regular graphs (dpeaa)DE-He213 Sparse random matrices (dpeaa)DE-He213 Poisson approximation (dpeaa)DE-He213 Linear eigenvalue statistics (dpeaa)DE-He213 Infinitely divisible distributions (dpeaa)DE-He213 |
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functional limit theorems for random regular graphs |
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Functional limit theorems for random regular graphs |
| abstract |
Abstract Consider %$d%$ uniformly random permutation matrices on %$n%$ labels. Consider the sum of these matrices along with their transposes. The total can be interpreted as the adjacency matrix of a random regular graph of degree %$2d%$ on %$n%$ vertices. We consider limit theorems for various combinatorial and analytical properties of this graph (or the matrix) as %$n%$ grows to infinity, either when %$d%$ is kept fixed or grows slowly with %$n%$. In a suitable weak convergence framework, we prove that the (finite but growing in length) sequences of the number of short cycles and of cyclically non-backtracking walks converge to distributional limits. We estimate the total variation distance from the limit using Stein’s method. As an application of these results we derive limits of linear functionals of the eigenvalues of the adjacency matrix. A key step in this latter derivation is an extension of the Kahn–Szemerédi argument for estimating the second largest eigenvalue for all values of %$d%$ and %$n%$. © Springer-Verlag 2012 |
| abstractGer |
Abstract Consider %$d%$ uniformly random permutation matrices on %$n%$ labels. Consider the sum of these matrices along with their transposes. The total can be interpreted as the adjacency matrix of a random regular graph of degree %$2d%$ on %$n%$ vertices. We consider limit theorems for various combinatorial and analytical properties of this graph (or the matrix) as %$n%$ grows to infinity, either when %$d%$ is kept fixed or grows slowly with %$n%$. In a suitable weak convergence framework, we prove that the (finite but growing in length) sequences of the number of short cycles and of cyclically non-backtracking walks converge to distributional limits. We estimate the total variation distance from the limit using Stein’s method. As an application of these results we derive limits of linear functionals of the eigenvalues of the adjacency matrix. A key step in this latter derivation is an extension of the Kahn–Szemerédi argument for estimating the second largest eigenvalue for all values of %$d%$ and %$n%$. © Springer-Verlag 2012 |
| abstract_unstemmed |
Abstract Consider %$d%$ uniformly random permutation matrices on %$n%$ labels. Consider the sum of these matrices along with their transposes. The total can be interpreted as the adjacency matrix of a random regular graph of degree %$2d%$ on %$n%$ vertices. We consider limit theorems for various combinatorial and analytical properties of this graph (or the matrix) as %$n%$ grows to infinity, either when %$d%$ is kept fixed or grows slowly with %$n%$. In a suitable weak convergence framework, we prove that the (finite but growing in length) sequences of the number of short cycles and of cyclically non-backtracking walks converge to distributional limits. We estimate the total variation distance from the limit using Stein’s method. As an application of these results we derive limits of linear functionals of the eigenvalues of the adjacency matrix. A key step in this latter derivation is an extension of the Kahn–Szemerédi argument for estimating the second largest eigenvalue for all values of %$d%$ and %$n%$. © Springer-Verlag 2012 |
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Functional limit theorems for random regular graphs |
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Johnson, Tobias Pal, Soumik Paquette, Elliot |
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| doi_str |
10.1007/s00440-012-0447-y |
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|
| score |
7.400769 |