The aim of this book is to investigate the spectral properties of random matrices (RM) when
their dimensions tend to infinity. All classical limiting theorems in statistics are under the …

In this paper, we give a brief review of the theory of spectral analysis of large dimensional
random matrices. Most of the existing work in the literature has been stated for real matrices …

Let {mij}, i= 1, 2,..., i= 1, 2,..., be iid random variables with Em11= 0 and Em21= a2. For each
n define Mn={mi} 1<, i,< n, the n X n matrix whose (i, j) component is m 1. We show that lim …

This paper proves almost-sure convergence of the empirical measure of the normalized
singular values of increasing rectangular submatrices of an infinite random matrix of …

Let U be a real nxn matrix whose entries uij are random variables, and let A and B be fixed n
xn real symmetric matrices. Statisticians (eg, see [OU]) have been interested in the …

In a multivariate analysis problem, we are given a sample x1, x2,..., xn of random
observations of dimension p. Statistical methods such as Principal Components Analysis …

Results on the analytic behavior of the limiting spectral distribution of matrices of sample
covariance type, studied in Marcenko and Pastur [2] and Yin [8], are derived. Through an …

A co-publication of the AMS and the Courant Institute of Mathematical Sciences at New York
University This book is a concise and self-contained introduction of recent techniques to …

Let X={X ij: i, j= 1, 2,…} be an infinite dimensional random matrix, T p be ap× p nonnegative
definite random matrix independent of X, for p= 1, 2,…. Suppose (1 p) tr T pk→ H k as as …

Abstract Let where Xn=(Xij) is n× N with iid complex standardized entries having finite fourth
moment, and is a Hermitian square root of the nonnegative definite Hermitian matrix Tn. The …