TY - JOUR
AB - We consider real symmetric or complex hermitian random matrices with correlated entries. We prove local laws for the resolvent and universality of the local eigenvalue statistics in the bulk of the spectrum. The correlations have fast decay but are otherwise of general form. The key novelty is the detailed stability analysis of the corresponding matrix valued Dyson equation whose solution is the deterministic limit of the resolvent.
AU - Ajanki, Oskari H
AU - Erdös, László
AU - Krüger, Torben H
ID - 429
IS - 1-2
JF - Probability Theory and Related Fields
SN - 01788051
TI - Stability of the matrix Dyson equation and random matrices with correlations
VL - 173
ER -