Universality results for largest eigenvalues of some sample covariance matrix ensembles

Details Universality results for largest eigenvalues of some sample covariance matrix ensembles Universality results for largest eigenvalues of some sample covariance matrix ensembles

2007-05-11

arxiv.org/abs/0705.1701v2

Mathematics

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3 figures 47 pages Simulations have been included, a mistake in the computation of the variance has been corrected (Section 2.

Scientific paper

For sample covariance matrices with iid entries with sub-Gaussian tails, when both the number of samples and the number of variables become large and the ratio approaches to one, it is a well-known result of A. Soshnikov that the limiting distribution of the largest eigenvalue is same as the of Gaussian samples. In this paper, we extend this result to two cases. The first case is when the ratio approaches to an arbitrary finite value. The second case is when the ratio becomes infinity or arbitrarily small.

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