FAST APPROACH TO THE TRACY-WIDOM LAW AT THE EDGE OF GOE AND GUE

被引：25

作者：

Johnstone, Iain M. ^{[1
]}

Ma, Zongming ^{[2
]}

机构：

[1] Stanford Univ, Dept Stat, Stanford, CA 94305 USA

[2] Univ Penn, Wharton Sch, Dept Stat, Philadelphia, PA 19104 USA

来源：

ANNALS OF APPLIED PROBABILITY | 2012年 / 22卷 / 05期

关键词：

Rate of convergence; random matrix; largest eigenvalue; LARGEST EIGENVALUE; SPACING DISTRIBUTIONS; RANDOM MATRICES; UNIVERSALITY; POLYNOMIALS; ENSEMBLES; LIMITS;

D O I：

10.1214/11-AAP819

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 study the rate of convergence for the largest eigenvalue distributions in the Gaussian unitary and orthogonal ensembles to their Tracy-Widom limits. We show that one can achieve an O(N-2/3.) rate with particular choices of the centering and scaling constants. The arguments here also shed light on more complicated cases of Laguerre and Jacobi ensembles, in both unitary and orthogonal versions. Numerical work shows that the suggested constants yield reasonable approximations, even for surprisingly small values of N.

引用

页码：1962 / 1988

页数：27

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