skip to content
Dominik Schröder

Correlated random matrices: Band rigidity and edge universality

Johannes Alt, László Erdős, Torben Krüger, Dominik Schröder

Ann. Probab.Vol. 48 (2020)


We prove that also the edge statistics of general correlated Hermitian random matrices are universal. Our result implies that the eigenvalues in each support interval of the asymptotic density is deterministic with high probability.


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.