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


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: 1432-2064
Publisher: Springer  
Date Published: 2018-01-01
Start Page: Epub ahead of print
Copyright Statement: CC BY
DOI: 10.1007/s00440-018-0835-z
Notes: Open access funding provided by Institute of Science and Technology (IST Austria).
Open access: yes (OA journal)
IST Austria Authors
  1. László Erdős
    110 Erdős
  2. Oskari Ajanki
    5 Ajanki
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