Universality of local eigenvalue statistics for some sample covariance matrices



We consider random, complex sample covariance matrices equation imageX*X, where X is a p × N random matrix with i.i.d. entries of distribution μ. It has been conjectured that both the distribution of the distance between nearest neighbor eigenvalues in the bulk and that of the smallest eigenvalues become, in the limit N → ∞, equation image → 1, the same as that identified for a complex Gaussian distribution μ. We prove these conjectures for a certain class of probability distributions μ. © 2004 Wiley Periodicals, Inc.