On universality of bulk local regime of the deformed Laguerre ensemble

Abstract:
We consider the deformed Laguerre Ensemble M = AA*/n + H in which H is a hermitian matrix (possibly random) and A is a m × n complex Gaussian random matrix (independent of H), m/n tends to c > 1 as n tends to infinity. Assuming that the Normalized Counting Measure of H converges weakly (with probability 1) to a non-random measure N with a bounded support we prove universality of the local eigenvalue statistics in the bulk of the limiting spectrum of M.

Presentation