Random covariance matrices: Universality of local statistics of eigenvalues

Terence Tao, Van Vu

We study the eigenvalues of the covariance matrix $\frac{1}{n}{M}^{\ast }M$ of a large rectangular matrix $M=M_{n,p}=(\hat{I}{\P }_{ij}{)}_{1\le i\le p;1\le j\le n}$ whose entries are i.i.d. rando…