Universality results for largest eigenvalues of some sample covariance matrix ensembles

Understand

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.