Convergence Rate of Expected Spectral Distributions of Large Random Matrices. Part I. Wigner Matrices
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.
Permanent link to this document: http://projecteuclid.org/euclid.aop/1176989261
Digital Object Identifier: doi:10.1214/aop/1176989261
Mathematical Reviews number (MathSciNet): MR1217559