Author(s):

Ajanki, Oskari H; Erdős, László; Krüger, Torben

Article Title: 
Stability of the matrix Dyson equation and random matrices with correlations

Affiliation 
IST Austria 
Abstract: 
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.

Keywords: 
Local law; Bulk universality; correlated random matrix

Journal Title:

Probability Theory and Related Fields

ISSN:

14322064

Publisher:

Springer

Date Published:

20180101

Start Page: 
Epub ahead of print

Copyright Statement: 
CC BY

DOI: 
10.1007/s004400180835z

Notes: 
Open access funding provided by Institute of Science and Technology (IST Austria).

Open access: 
yes (OA journal) 