Shape fluctuations and random matrices

被引：938

作者：

Johansson, K ^{[1
]}

机构：

[1] Royal Inst Technol, Dept Math, S-10044 Stockholm, Sweden

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2000年 / 209卷 / 02期

关键词：

D O I：

10.1007/s002200050027

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We study a certain random growth model in two dimensions closely related to the one-dimensional totally asymmetric exclusion process. The results show that the shape fluctuations, appropriately scaled, converges in distribution to the Tracy-Widom largest eigenvalue distribution for the Gaussian Unitary Ensemble (GUE).

引用

页码：437 / 476

页数：40

共 17 条

[1] On the distribution of the length of the longest increasing subsequence of random permutations
Baik, J
Deift, P
Johansson, K
[J]. JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 1999, 12 (04) : 1119 - 1178
[2] BenArous G, 1997, PROBAB THEORY REL, V108, P517
[3] Constrained energy problems with applications to orthogonal polynomials of a discrete variable
Dragnev, PD
Saff, EB
[J]. JOURNAL D ANALYSE MATHEMATIQUE, 1997, 72 (1): : 223 - 259
[4] DISTRIBUTIONS OF MATRIX VARIATES + LATENT ROOTS DERIVED FROM NORMAL SAMPLES
JAMES, AT
[J]. ANNALS OF MATHEMATICAL STATISTICS, 1964, 35 (02): : 475 - &
[5] Uniform asymptotic expansions for Meixner polynomials
Jin, XS
Wong, R
[J]. CONSTRUCTIVE APPROXIMATION, 1998, 14 (01) : 113 - 150
[6] On fluctuations of eigenvalues of random hermitian matrices
Johansson, K
[J]. DUKE MATHEMATICAL JOURNAL, 1998, 91 (01) : 151 - 204
[7] PERMUTATIONS, MATRICES, AND GENERALIZED YOUNG TABLEAUX
KNUTH, DE
[J]. PACIFIC JOURNAL OF MATHEMATICS, 1970, 34 (03) : 709 - &
[8] KRUG J, 1992, SOLIDS FAR EQUILIBRI, P479
[9] THE SMALL DISPERSION LIMIT OF THE KORTEWEG-DEVRIES EQUATION .1.
LAX, PD
LEVERMORE, CD
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1983, 36 (03) : 253 - 290
[10] DIVERGENCE OF SHAPE FLUCTUATIONS IN 2 DIMENSIONS
NEWMAN, CM
PIZA, MST
[J]. ANNALS OF PROBABILITY, 1995, 23 (03) : 977 - 1005

← 1 2 →