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

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