Asymptotic distribution of singular values for matrices in a spherical ensemble

被引：0

作者：

Tikhomirov A.N. ^{[1
]}

机构：

[1] Department of Mathematics, Komi Scientific Center of UBRAS, Syktyvkar

来源：

Siberian Advances in Mathematics | 2014年 / 24卷 / 4期

基金：

俄罗斯基础研究基金会;

关键词：

empirical spectral distribution function; random matrix; spherical ensemble; spherical law;

D O I：

10.3103/S105513441404004X

中图分类号：

学科分类号：

摘要：

We consider the asymptotic behavior of the singular values of a so-called spherical ensemble of random matrices of large dimension. These are matrices of the form XY-1, where X and Y are independent matrices of dimension n × n whose symmetric entries have correlation coefficient ρ. We show that the limit distribution of the singular values is independent of the correlation coefficient and has the density where stands for the indicator of an event A. © 2014, Allerton Press, Inc.

引用

页码：282 / 303

页数：21

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