Random matrix central limit theorems for nonintersecting random walks

被引：27

作者：

Baik, Jinho ^{[1
]}

Suidan, Toufic M.

机构：

[1] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

[2] Univ Calif Santa Cruz, Dept Math, Santa Cruz, CA 95064 USA

来源：

ANNALS OF PROBABILITY | 2007年 / 35卷 / 05期

关键词：

nonintersecting random walks; Tracy-Widom distribution; sine kernel; strong approximation; Riemann-Hilbert problem; Stieltjes-Wigert polynomials;

D O I：

10.1214/009117906000001105

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We consider nonintersecting random walks satisfying the condition that the increments have a finite moment generating function. We prove that in a certain limiting regime where the number of walks and the number of time steps grow to infinity, several limiting distributions of the walks at the mid-time behave as the eigenvalues of random Hermitian matrices as the dimension of the matrices grows to infinity.

引用

页码：1807 / 1834

页数：28

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