On the Empirical Distribution of Eigenvalues of a Class of Large Dimensional Random Matrices

J. W. Silverstein and Z. D. Bai

Journal of Multivariate Analysis, 1995, vol. 54, issue 2, 175-192

Abstract: A stronger result on the limiting distribution of the eigenvalues of random Hermitian matrices of the form A + XTX*, originally studied in Marcenko and Pastur, is presented. Here, X(N - n), T(n - n), and A(N - N) are independent, with X containing i.i.d. entries having finite second moments, T is diagonal with real (diagonal) entries, A is Hermitian, and n/N --> c > 0 as N --> [infinity]. Under additional assumptions on the eigenvalues of A and T, almost sure convergence of the empirical distribution function of the eigenvalues of A + XTX* is proven with the aid of Stieltjes transforms, taking a more direct approach than previous methods.

Date: 1995
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