THE CIRCULAR LAW FOR RANDOM MATRICES

被引：108

作者：

Gotze, Friedrich ^{[1
]}

Tikhomirov, Alexander ^{[2
]}

机构：

[1] Univ Bielefeld, Fac Math, D-4800 Bielefeld, Germany

[2] Sankt Peterburg State Univ, Fac Math & Mech, St Petersburg, Russia

来源：

ANNALS OF PROBABILITY | 2010年 / 38卷 / 04期

关键词：

Circular law; random matrices; INVERTIBILITY;

D O I：

10.1214/09.AOP522

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 consider the joint distribution of real and imaginary parts of eigen-values of random matrices with Independent entries with mean zero and unit variance We prove the convergence of this distribution to the uniform distribution on the unit disc without assumptions on the existence of a density for the distribution of entries We assume that the entries have a finite moment of order larger than two and consider the case of sparse matrices The results are based on previous work of Bai, Rudelson and the authors extending those results to a larger class of sparse matrices

引用

页码：1444 / 1491

页数：48

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