The Edge Universality of Correlated Matrices
arXiv:1712.04889
Abstract
We consider a Gaussian random matrix with correlated entries that have a power law decay of order and prove universality for the extreme eigenvalues. A local law is proved using the self-consistent equation combined with a decomposition of the matrix. This local law along with concentration of eigenvalues around the edge allows us to get an bound for extreme eigenvalues. Using a recent result of the Dyson-Brownian motion, we prove universality of extreme eigenvalues.
24 pages, added references, simplified Lemma 3.9