# On the empirical distribution of eigenvalues of a class of large dimensional random matrices

@article{Silverstein1995OnTE, title={On the empirical distribution of eigenvalues of a class of large dimensional random matrices}, author={Jack W. Silverstein and Zhidong Bai}, journal={Journal of Multivariate Analysis}, year={1995}, volume={54}, pages={175-192} }

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…

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