SUBORDINATION FOR THE SUM OF TWO RANDOM MATRICES

被引：22

作者：

Kargin, V. ^{[1
]}

机构：

[1] Ctr Math Sci, Stat Lab, Cambridge CB3 0WB, England

来源：

ANNALS OF PROBABILITY | 2015年 / 43卷 / 04期

关键词：

Random matrices; subordination; small-rank matrix deformations; delocalization; local limit law; FINITE RANK DEFORMATIONS; LARGEST EIGENVALUE; FREE CONVOLUTION; WIGNER MATRICES; PERTURBATIONS; EIGENVECTORS; LAW;

D O I：

10.1214/14-AOP929

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：

This paper is about the relation of random matrix theory and the subordination phenomenon in complex analysis. We find that the resolvent of the sum of two random matrices is approximately subordinated to the resolvents of the original matrices. We estimate the error terms in this relation and in the subordination relation for the traces of the resolvents. This allows us to prove a local limit law for eigenvalues and a delocalization result for eigenvectors of the sum of two random matrices. In addition, we use subordination to determine the limit of the largest eigenvalue for the rank-one deformations of unitary-invariant random matrices.

引用

收藏

页码：2119 / 2150

页数：32

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