We consider the deformed Gaussian ensemble Hn=Hn (0) + Mn in which Hn (0) is a hermitian matrix (possibly random) and Mn is the Gaussian unitary random matrix (GUE) independent of Hn (0). Assuming that the Normalized Counting Measure of Hn (0) converges weakly (in probability if random) to a non-random measure N(0) with a bounded support and assuming some conditions on the convergence rate, we prove the universality of the local eigenvalue statistics near the edge of the limiting spectrum of Hn.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
- Airy kernel
- Deformed GUE
- Edge universality
- Random matrices