Small deviations for beta ensembles

被引：67

作者：

Ledoux, Michel ^{[1
]}

Rider, Brian ^{[2
]}

机构：

[1] Univ Toulouse, Inst Math Toulouse, F-31062 Toulouse, France

[2] Univ Colorado, Dept Math, Boulder, CO 80309 USA

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2010年 / 15卷

基金：

美国国家科学基金会;

关键词：

Random matrices; eigenvalues; small deviations; DISTRIBUTIONS; EIGENVALUE; INEQUALITIES; MATRICES; EDGE;

D O I：

10.1214/EJP.v15-798

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 establish various small deviation inequalities for the extremal (soft edge) eigenvalues in the beta-Hermite and beta-Laguerre ensembles. In both settings, upper bounds on the variance of the largest eigenvalue of the anticipated order follow immediately.

引用

页码：1319 / 1343

页数：25

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