CONVERGENCE RATE OF EXPECTED SPECTRAL DISTRIBUTIONS OF LARGE RANDOM MATRICES .1. WIGNER MATRICES

被引：66

作者：

BAI, ZD

机构：

来源：

ANNALS OF PROBABILITY | 1993年 / 21卷 / 02期

关键词：

BERRY-ESSEEN INEQUALITY; CONVERGENCE RATE; LARGE DIMENSIONAL RANDOM MATRIX; MARCHENKO-PASTUR DISTRIBUTION; SAMPLE COVARIANCE MATRIX; SEMICIRCULAR LAW; SPECTRAL ANALYSIS; STIELTJES TRANSFORM; WIGNER MATRIX;

D O I：

10.1214/aop/1176989261

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：

In this paper, we shall develop certain inequalities to bound the difference between distributions in terms of their Stieltjes transforms. Using these inequalities, convergence rates of expected spectral distributions of large dimensional Wigner and sample covariance matrices are established. The paper is organized into two parts. This is the first part, which is devoted to establishing the basic inequalities and a convergence rate for Wigner matrices.

引用

页码：625 / 648

页数：24

共 30 条

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