Shape fluctuations and random matrices

被引：946

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 [J].

Baik, J ;

Deift, P ;

Johansson, K .

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 [J].

Dragnev, PD ;

Saff, EB .

JOURNAL D ANALYSE MATHEMATIQUE, 1997, 72 (1) :223-259

[4] DISTRIBUTIONS OF MATRIX VARIATES + LATENT ROOTS DERIVED FROM NORMAL SAMPLES [J].

JAMES, AT .

ANNALS OF MATHEMATICAL STATISTICS, 1964, 35 (02) :475-&

[5] Uniform asymptotic expansions for Meixner polynomials [J].

Jin, XS ;

Wong, R .

CONSTRUCTIVE APPROXIMATION, 1998, 14 (01) :113-150

[6] On fluctuations of eigenvalues of random hermitian matrices [J].

Johansson, K .

DUKE MATHEMATICAL JOURNAL, 1998, 91 (01) :151-204

[7] PERMUTATIONS, MATRICES, AND GENERALIZED YOUNG TABLEAUX [J].

KNUTH, DE .

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. [J].

LAX, PD ;

LEVERMORE, CD .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1983, 36 (03) :253-290

[10] DIVERGENCE OF SHAPE FLUCTUATIONS IN 2 DIMENSIONS [J].

NEWMAN, CM ;

PIZA, MST .

ANNALS OF PROBABILITY, 1995, 23 (03) :977-1005

← 1 2 →