Correlated Random Matrices: Band Rigidity and Edge Universality
Probability
2023-01-11 v4 Mathematical Physics
math.MP
Abstract
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.
Cite
@article{arxiv.1804.07744,
title = {Correlated Random Matrices: Band Rigidity and Edge Universality},
author = {Johannes Alt and László Erdős and Torben Krüger and Dominik Schröder},
journal= {arXiv preprint arXiv:1804.07744},
year = {2023}
}
Comments
26 pages. In the new version we included a self-contained analysis of general square-root edges of the density of states