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.
Publié le : 1993-04-14
Classification:
Berry-Esseen inequality,
convergence rate,
large dimensional random matrix,
Marchenko-Pastur distribution,
sample covariance matrix,
semicircular law,
spectral analysis,
Stieltjes transform,
Wigner matrix,
60F15,
62F15
@article{1176989261,
author = {Bai, Z. D.},
title = {Convergence Rate of Expected Spectral Distributions of Large Random Matrices. Part I. Wigner Matrices},
journal = {Ann. Probab.},
volume = {21},
number = {4},
year = {1993},
pages = { 625-648},
language = {en},
url = {http://dml.mathdoc.fr/item/1176989261}
}
Bai, Z. D. Convergence Rate of Expected Spectral Distributions of Large Random Matrices. Part I. Wigner Matrices. Ann. Probab., Tome 21 (1993) no. 4, pp. 625-648. http://gdmltest.u-ga.fr/item/1176989261/