The Annals of Probability

Convergence Rate of Expected Spectral Distributions of Large Random Matrices. Part I. Wigner Matrices

Z. D. Bai

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Probab., Volume 21, Number 2 (1993), 625-648.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176989261

Digital Object Identifier
doi:10.1214/aop/1176989261

Mathematical Reviews number (MathSciNet)
MR1217559

Zentralblatt MATH identifier
0779.60024

JSTOR
links.jstor.org

Subjects
Primary: 60F15: Strong theorems
Secondary: 62F15: Bayesian inference

Keywords
Berry-Esseen inequality convergence rate large dimensional random matrix Marchenko-Pastur distribution sample covariance matrix semicircular law spectral analysis Stieltjes transform Wigner matrix

Citation

Bai, Z. D. Convergence Rate of Expected Spectral Distributions of Large Random Matrices. Part I. Wigner Matrices. Ann. Probab. 21 (1993), no. 2, 625--648. doi:10.1214/aop/1176989261. https://projecteuclid.org/euclid.aop/1176989261


Export citation

See also

  • Part II: Z. D. Bai. Convergence Rate of Expected Spectral Distributions of Large Random Matrices. Part II. Sample Covariance Matrices. Ann. Probab., Volume 21, Number 2 (1993), 649--672.