Universality of local eigenvalue statistics for some sample covariance matrices

We consider random, complex sample covariance matrices 1/N X*X, where X is a p x N random matrix with i.i.d. entries of distribution mu. 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 -> infinity, P/N -> 1, the same as that identified for a complex Gaussian distribution mu. We prove these conjectures for a certain class of probability distributions mu. (c) 2004 Wiley Periodicals, Inc.