A NOTE ON THE CENTRAL LIMIT THEOREM FOR THE EIGENVALUE COUNTING FUNCTION OF WIGNER MATRICES

被引：11
|
作者：
Dallaporta, Sandrine [1 ]
Vu, Van [2 ]
机构：
[1] Univ Toulouse, CNRS, UMR 5219, Inst Math Toulouse, F-31062 Toulouse, France
[2] Rutgers State Univ, Dept Math, Piscataway, NJ 08854 USA
来源：
ELECTRONIC COMMUNICATIONS IN PROBABILITY | 2011年 / 16卷
关键词：
random matrices; eigenvalue counting function; Central Limit Theorem; Four Moment Theorem; localization; GAUSSIAN FLUCTUATIONS;
D O I：
10.1214/ECP.v16-1634
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：
The purpose of this note is to establish a Central Limit Theorem for the number of eigenvalues of a Wigner matrix in an interval. The proof relies on the correct asymptotics of the variance of the eigenvalue counting function of GUE matrices due to Gustavsson, and its extension to large families of Wigner matrices by means of the Tao and Vu Four Moment Theorem and recent localization results by Erdos, Yau and Yin.
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页码：314 / 322
页数：9
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