We consider the Hermitian sample covariance matrices Hn=m-1Σn1/2Am,nAm,n*Σn1/2 in which Σn is a positive definite Hermitian matrix (possibly random) and Am,n is a n×m complex Gaussian random matrix (independent of Σn), and m→∞, n→∞, such that mn-1→c>1. Assuming that the normalized counting measure of Σn converges weakly (in probability) to a nonrandom measure N(0) with a bounded support, we prove the universality of the local eigenvalue statistics in the bulk of the limiting spectrum of Hn.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics