Convergence rate for spectral distribution of addition of random matrices

被引：10

作者：

Bao, Zhigang ^{[1
]}

Erdos, Laszlo ^{[2
]}

Schnelli, Kevin ^{[3
]}

机构：

[1] HKUST, Hong Kong, Hong Kong, Peoples R China

[2] IST Austria, Klosterneuburg, Austria

[3] KTH Royal Inst Technol, Stockholm, Sweden

来源：

ADVANCES IN MATHEMATICS | 2017年 / 319卷

关键词：

Random matrices; Strong local law; Free convolution; Convergence rate; FREE PROBABILITY; SUBORDINATION; CONVOLUTION;

D O I：

10.1016/j.aim.2017.08.028

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let A and B be two N by N deterministic Hermitian matrices and let U be an N by N Haar distributed unitary matrix. It is well known that the spectral distribution of the sum H = A UBU* converges weakly to the free additive convolution of the spectral distributions of A and B, as N tends to infinity. We establish the optimal convergence rate 1/N in the bulk of the spectrum. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：251 / 291

页数：41

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