On the Empirical Distribution of Eigenvalues of a Class of Large Dimensional Random Matrices
نویسنده
چکیده
A stronger result on the limiting distribution of the eigenvalues of random Hermitian matrices of the form A+XTX∗, originally studied in Marčenko and Pastur [4], 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 → ∞. Under addtional 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.
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تاریخ انتشار 1995