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RANDOM MATRICES WITH SLOW CORRELATION DECAY

Part of: Special matrices Probability theory on algebraic and topological structures

Published online by Cambridge University Press:  26 March 2019

LÁSZLÓ ERDŐS Open the ORCID record for LÁSZLÓ ERDŐS [Opens in a new window] ,
TORBEN KRÜGER  and
DOMINIK SCHRÖDER Open the ORCID record for DOMINIK SCHRÖDER [Opens in a new window]
LÁSZLÓ ERDŐS
Affiliation:
IST Austria, 3400 Klosterneuburg, Austria; lerdos@ist.ac.at, dschroed@ist.ac.at
TORBEN KRÜGER
Affiliation:
University of Bonn, 53115 Bonn, Germany; torben.krueger@uni-bonn.de
DOMINIK SCHRÖDER
Affiliation:
IST Austria, 3400 Klosterneuburg, Austria; lerdos@ist.ac.at, dschroed@ist.ac.at

Abstract

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We consider large random matrices with a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent away from the spectral edges, generalizing the recent result of Ajanki et al. [‘Stability of the matrix Dyson equation and random matrices with correlations’, Probab. Theory Related Fields173(1–2) (2019), 293–373] to allow slow correlation decay and arbitrary expectation. The main novel tool is a systematic diagrammatic control of a multivariate cumulant expansion.

MSC classification

Primary: 60B20: Random matrices (probabilistic aspects; for algebraic aspects see ) 15B52: Random matrices
Type
Research Article
Information
Forum of Mathematics, Sigma , Volume 7 , 2019 , e8
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s) 2019

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