Correlated Random Matrices: Band Rigidity and Edge Universality

Johannes Alt, László Erdős, Torben Krüger, Dominik Schröder

Published 2018-04-20Version 1

We prove edge universality for a general class of correlated real symmetric or complex Hermitian Wigner matrices with arbitrary expectation. Contrary to previous results, even for independent Wigner ensembles, our theorem also applies to internal edges of the self consistent density. The main technical novelty lies in establishing a strong form of band rigidity which excludes mismatches between location and label of eigenvalues close to internal edges.