메뉴 건너뛰기




Volumn 24, Issue 4, 2011, Pages 919-944

Beta ensembles, stochastic airy spectrum, and a diffusion

Author keywords

[No Author keywords available]

Indexed keywords


EID: 79959893612     PISSN: 08940347     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0894-0347-2011-00703-0     Document Type: Article
Times cited : (242)

References (33)
  • 1
    • 0033443150 scopus 로고    scopus 로고
    • On the distribution of the length of the longest increasing subsequence of random permutations
    • MR1682248 (2000e:05006)
    • J. Baik, P. Deift, K. Johansson, On the distribution of the length of the longest increasing subsequence of random permutations. J. Amer.Math. Soc. 12 (1999), 1119-1178. MR1682248 (2000e:05006)
    • (1999) J. Amer.Math. Soc , vol.12 , pp. 1119-1178
    • Baik, J.1    Deift, P.2    Johansson, K.3
  • 2
    • 27644476898 scopus 로고    scopus 로고
    • Phase transition of the largest eigenvalue for non null complex sample covariance matrices
    • MR2165575, 2006g:15046
    • J. Baik, G. Ben Arous, S. Péché, Phase transition of the largest eigenvalue for non null complex sample covariance matrices. Ann. Probab. 33 (2005), 1643-1697. MR2165575 (2006g:15046)
    • (2005) Ann. Probab , vol.33 , pp. 1643-1697
    • Baik, J.1    Ben, A.G.2    Péché, S.3
  • 3
    • 42449142926 scopus 로고    scopus 로고
    • Asymptotics of Tracy-Widom distributions and the total integral of a Painlev́e II function
    • MR2395479 (2009e:33068)
    • J. Baik, R. Buckingham, J. DiFranco, Asymptotics of Tracy-Widom distributions and the total integral of a Painlev́e II function. Comm. Math. Phys., 280 (2008), 463-497. MR2395479 (2009e:33068)
    • (2008) Comm. Math. Phys , vol.280 , pp. 463-497
    • Baik, J.1    Buckingham, R.2    Difranco, J.3
  • 4
    • 0035580083 scopus 로고    scopus 로고
    • GUEs and queues
    • MR1818248 (2002a:60165)
    • Y. Baryshnikov, GUEs and queues. Probab. Theory Rel. Fields. 119 (2001), 256-274. MR1818248 (2002a:60165)
    • (2001) Probab. Theory Rel. Fields , vol.119 , pp. 256-274
    • Baryshnikov, Y.1
  • 5
    • 0033434198 scopus 로고    scopus 로고
    • The Ground State Eigenvalue of Hill's Equation with White Noise Potential
    • MR1699969 (2001g:60158)
    • S. Cambronero, H.P. McKean, The Ground State Eigenvalue of Hill's Equation with White Noise Potential. Comm. Pure Appl. Math. 52 (1999), no 10, 1277-1294. MR1699969 (2001g:60158)
    • (1999) Comm. Pure Appl. Math , vol.52 , Issue.10 , pp. 1277-1294
    • Cambronero, S.1    McKean, H.P.2
  • 6
    • 33744546387 scopus 로고    scopus 로고
    • On the shape of the ground state eigenvalue density of a random Hill's equation
    • MR2222441 (2007a:34036a)
    • S. Cambronero, J. Ramírez, B. Rider, On the shape of the ground state eigenvalue density of a random Hill's equation. Comm. Pure Appl Math. 59 (2006), 935-976. MR2222441 (2007a:34036a)
    • (2006) Comm. Pure Appl Math , vol.59 , pp. 935-976
    • Cambronero, S.1    Ramírez, J.2    Rider, B.3
  • 9
    • 33646069301 scopus 로고    scopus 로고
    • Hermite and Laguerre β-ensembles: Asymptotic corrections to the eigenvalue density
    • MR2227950 (2007f:82043)
    • P. Desrosiers, P. Forrester, Hermite and Laguerre β-ensembles: asymptotic corrections to the eigenvalue density. Nuc. Phys. B. 743 (2006), 307-332. MR2227950 (2007f:82043)
    • (2006) Nuc. Phys. B , vol.743 , pp. 307-332
    • Desrosiers, P.1    Forrester, P.2
  • 10
    • 28444496679 scopus 로고    scopus 로고
    • Distribution functions for edge eigenvalues in Orthogonal and Symplectic Ensembles: Painlev́e representations
    • MR2181265 (2006h:60014)
    • M. Dieng, Distribution functions for edge eigenvalues in Orthogonal and Symplectic Ensembles: Painlev́e representations. Int. Math. Res. Notices. 2005, 2263-2287. MR2181265 (2006h:60014)
    • (2005) Int. Math. Res. Notices , pp. 2263-2287
    • Dieng, M.1
  • 12
    • 0036850051 scopus 로고    scopus 로고
    • Matrix models for beta ensembles
    • MR1936554 (2004g:82044)
    • I. Dumitriu, A. Edelman, Matrix models for beta ensembles. J. Math. Phys. 43 (2002), 5830-5847. MR1936554 (2004g:82044)
    • (2002) J. Math. Phys , vol.43 , pp. 5830-5847
    • Dumitriu, I.1    Edelman, A.2
  • 13
    • 79959873666 scopus 로고    scopus 로고
    • Master's thesis, Ecole Normale Sup ́erieure
    • L. Dumaz, The Tracy-Widom right tail. Master's thesis, Ecole Normale Sup ́erieure, 2009.
    • (2009) The Tracy-Widom Right Tail
    • Dumaz, L.1
  • 14
    • 79959881172 scopus 로고    scopus 로고
    • The right tail exponent of the Tracy-Widom-beta distribution
    • arXiv
    • L. Dumav, B. Viŕag The right tail exponent of the Tracy-Widom-beta distribution. Preprint, arXiv:1102.4818 (2011).
    • (2011) Preprint , vol.1102 , pp. 4818
    • Dumav, L.1    Viŕag, B.2
  • 15
    • 34249901791 scopus 로고    scopus 로고
    • From random matrices to stochastic operators
    • MR2331033 (2009b:82037)
    • A. Edelman, B. Sutton, From random matrices to stochastic operators. J. Stat. Phys. 127 (2007), 1121-1165. MR2331033 (2009b:82037)
    • (2007) J. Stat. Phys , vol.127 , pp. 1121-1165
    • Edelman, A.1    Sutton, B.2
  • 17
    • 46749089905 scopus 로고    scopus 로고
    • Tracy-Widom limit for the largest eigenvalue of a large class of complex Wishart matrices
    • MR2308592 (2007m:60057)
    • N. El Karoui, Tracy-Widom limit for the largest eigenvalue of a large class of complex Wishart matrices. Ann. Probab. 35 (2007), 663-714. MR2308592 (2007m:60057)
    • (2007) Ann. Probab , vol.35 , pp. 663-714
    • el Karoui, N.1
  • 19
    • 33646754970 scopus 로고    scopus 로고
    • Scaling limit for the space-time covariance of the stationary totally asymmetric simple exclusion process
    • MR2217295 (2007g:82038a)
    • P. Ferrari, H. Spohn, Scaling limit for the space-time covariance of the stationary totally asymmetric simple exclusion process. Comm. Math. Phys. 265 (2006), 1-44. MR2217295 (2007g:82038a)
    • (2006) Comm. Math. Phys , vol.265 , pp. 1-44
    • Ferrari, P.1    Spohn, H.2
  • 20
    • 84874083594 scopus 로고    scopus 로고
    • London Math. Soc, Monographs, Princeton University Press, MR2641363 (2011d:82001)
    • P. Forrester, Log-Gases and Random Matrices. London Math. Soc. Monographs, Princeton University Press, 2010. MR2641363 (2011d:82001)
    • (2010) Log-Gases and Random Matrices
    • Forrester, P.1
  • 21
    • 36149013627 scopus 로고
    • Green's functions for a particle in a one-dimensional random potential
    • MR0187859 (32:5304)
    • B.I. Halperin, Green's functions for a particle in a one-dimensional random potential. Phys. Rev. (2) 139 (1965), A104-A117. MR0187859 (32:5304)
    • (1965) Phys. Rev , vol.139 , Issue.2
    • Halperin, B.I.1
  • 22
    • 0034340689 scopus 로고    scopus 로고
    • Shape fluctuations and random matrices
    • MR1737991 (2001h:60177)
    • K. Johansson, Shape fluctuations and random matrices. Comm. Math. Phys. 209 (2000), 437-476. MR1737991 (2001h:60177)
    • (2000) Comm. Math. Phys , vol.209 , pp. 437-476
    • Johansson, K.1
  • 23
    • 0035641726 scopus 로고    scopus 로고
    • On the distribution of the largest eigenvalue in principal components analysis
    • MR1863961 (2002i:62115)
    • I.M. Johnstone, On the distribution of the largest eigenvalue in principal components analysis. Ann. Statist. 29 (2001), 295-327. MR1863961 (2002i:62115)
    • (2001) Ann. Statist , vol.29 , pp. 295-327
    • Johnstone, I.M.1
  • 24
    • 70350662136 scopus 로고    scopus 로고
    • Eigenvalue Statistics for CMV Matrices: From Poisson to Clock via Random Matrix Ensembles
    • MR2484278 (2009k:81087)
    • S. Killip, M. Stoiciu, Eigenvalue Statistics for CMV Matrices: From Poisson to Clock via Random Matrix Ensembles. Duke Math. Journal 146 (2009), 361-399. MR2484278 (2009k:81087)
    • (2009) Duke Math. Journal , vol.146 , pp. 361-399
    • Killip, S.1    Stoiciu, M.2
  • 25
    • 21344487105 scopus 로고
    • A limit law for the ground state of Hill's equation
    • MR1268791 (95d:82036)
    • H.P. McKean, A limit law for the ground state of Hill's equation. J. Stat. Phys. 74 (1994), 1227-1232. MR1268791 (95d:82036)
    • (1994) J. Stat. Phys , vol.74 , pp. 1227-1232
    • McKean, H.P.1
  • 26
    • 0141450340 scopus 로고    scopus 로고
    • Scale invariance of the PNG droplet and the Airy process
    • MR1933446 (2003i:82050)
    • M. Prähofer, H. Spohn, Scale invariance of the PNG droplet and the Airy process. J. Stat. Phys. 108 (2002), 1071-1106. MR1933446 (2003i:82050)
    • (2002) J. Stat. Phys , vol.108 , pp. 1071-1106
    • Prähofer, M.1    Spohn, H.2
  • 27
    • 67349160712 scopus 로고    scopus 로고
    • Diffusion at the random matrix hard edge
    • MR2504858 (2010g:47083)
    • J. Ramírez, B. Rider, Diffusion at the random matrix hard edge. Comm. Math. Phys. 288 (2009), 887-906 MR2504858 (2010g:47083)
    • (2009) Comm. Math. Phys , vol.288 , pp. 887-906
    • Ramírez, J.1    Rider, B.2
  • 29
    • 27644532196 scopus 로고
    • Level spacing distributions and the Airy kernel
    • MR1257246 (95e:82003)
    • C. Tracy, H. Widom, Level spacing distributions and the Airy kernel. Comm. Math. Phys. 159 (1994), 151-174. MR1257246 (95e:82003)
    • (1994) Comm. Math. Phys , vol.159 , pp. 151-174
    • Tracy, C.1    Widom, H.2
  • 30
    • 0030545965 scopus 로고    scopus 로고
    • On orthogonal and symplectic matrix ensembles
    • MR1385083 (97a:82055)
    • C. Tracy, H. Widom On orthogonal and symplectic matrix ensembles. Comm. Math. Phys. 177 (1996), 727-754. MR1385083 (97a:82055)
    • (1996) Comm. Math. Phys , vol.177 , pp. 727-754
    • Tracy, C.1    Widom, H.2
  • 31
    • 0011438216 scopus 로고
    • Eigenvalue distributions of large Hermitian matrices; Wigner's semicircle law and a theorem of Kac, Murdock, and Szeg{double acute accent}o
    • 1984, MR761763 (86c:60055)
    • H. F. Trotter, (1984) Eigenvalue distributions of large Hermitian matrices; Wigner's semicircle law and a theorem of Kac, Murdock, and Szeg{double acute accent}o. Adv. in Math. 54 (1984), 67-82. MR761763 (86c:60055)
    • (1984) Adv. in Math , vol.54 , pp. 67-82
    • Trotter, H.F.1
  • 32
    • 70350639757 scopus 로고    scopus 로고
    • Continuum limits of random matrices and the Brownian carousel
    • MR2534097 (2011d:60023)
    • B. Valko, B. Virág, Continuum limits of random matrices and the Brownian carousel. Inventiones 177 (2009), 463-508. MR2534097 (2011d:60023)
    • (2009) Inventiones , vol.177 , pp. 463-508
    • Valko, B.1    Virág, B.2
  • 33
    • 77957037478 scopus 로고    scopus 로고
    • Large gaps between random eigenvalues
    • MR2674999
    • B. Valko, B. Virág, Large gaps between random eigenvalues. Ann. Probab. 38 (2010), 1263-1279. MR2674999
    • (2010) Ann. Probab , vol.38 , pp. 1263-1279
    • Valko, B.1    Virág, B.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.