Local semicircle law with imprimitive variance matrix

被引：6

作者：

Ajanki, Oskari ^{[1
]}

Erdos, Laszlo ^{[1
]}

Krueger, Torben ^{[1
]}

机构：

[1] IST Austria, A-3400 Klosterneuburg, Austria

来源：

ELECTRONIC COMMUNICATIONS IN PROBABILITY | 2014年 / 19卷

关键词：

Generalised Wigner matrices; generalised random sample covariance matrices; hard edge; local semicircle law; UNIVERSALITY;

D O I：

10.1214/ECP.v19-3121

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 extend the proof of the local semicircle law for generalized Wigner matrices given in [4] to the case when the matrix of variances has an eigenvalue -1. In particular, this result provides a short proof of the optimal local Marchenko-Pastur law at the hard edge (i.e. around zero) for sample covariance matrices X*X, where the variances of the entries of X may vary.

引用

页码：1 / 9

页数：9

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