Small deviations for beta ensembles

被引：66
|
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
收藏
页码：1319 / 1343
页数：25
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