On the empirical distribution of eigenvalues of a class of large dimensional random matrices
Journal of Multivariate Analysis
Convergence Rates of Spectral Distributions of Large Sample Covariance Matrices
SIAM Journal on Matrix Analysis and Applications
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We consider non-white Wishart ensembles 1pX@SX^*, where X is a pxN random matrix with i.i.d. complex standard Gaussian entries and @S is a covariance matrix, with fixed eigenvalues, close to the identity matrix. We prove that the largest eigenvalue of such random matrix ensembles exhibits a universal behavior in the large-N limit, provided @S is ''close enough'' to the identity matrix. If not, we identify the limiting distribution of the largest eigenvalues, focusing on the case where the largest eigenvalues almost surely exit the support of the limiting Marchenko-Pastur's distribution.