We prove edge universality for a general class of correlated real symmetric or complex Hermitian Wigner matrices with arbitrary expectation. Our theorem also applies to internal edges of the self-consistent density of states. In particular, we establish a strong form of band rigidity which excludes mismatches between location and label of eigenvalues close to internal edges in these general models.
"Correlated random matrices: Band rigidity and edge universality." Ann. Probab. 48 (2) 963 - 1001, March 2020. https://doi.org/10.1214/19-AOP1379