Bulk universality for deformed Wigner matrices
type: Item
instance of: scholarly article
title: Bulk universality for deformed Wigner matrices
zbMATH Open document ID: 1346.15037
DOI: 10.1214/15-AOP1023
author: Ji Oon Lee
author: Kevin Schnelli
author: Ben Stetler
author: Horng-Tzer Yau
published in: The Annals of Probability
publication date: 2016-07-14T00:00:00Z
full work available at URL: https://arxiv.org/abs/1405.6634
full work available at URL: https://projecteuclid.org/euclid.aop/1463410044
review text: The authors consider \(N\times N\) random matrices of the form \(H=W+V\) where \(W\) is a real symmetric or complex Hermitian Wigner matrix and \(V\) is a random or deterministic real diagonal matrix whose entries are independent of \(W\). Subexponential decay for the matrix entries of \(W\) is assumed, and \(V\) is chosen so that the eigenvalues of \(W\) and \(V\) are typically of the same order. For a large class of diagonal matrices \(V\), it is shown that the local statistics in the bulk of the spectrum are universal in the limit of large \(N\).
Mathematics Subject Classification ID: 15B52
Mathematics Subject Classification ID: 60B20
Mathematics Subject Classification ID: 82B44
Mathematics Subject Classification ID: 60F99
Mathematics Subject Classification ID: 15A18
zbMATH DE Number: 6603574
zbMATH Keywords: random matrix
zbMATH Keywords: local semicircle law
zbMATH Keywords: universality
zbMATH Keywords: complex Hermitian Wigner matrix
zbMATH Keywords: eigenvalue
reviewed by: Andreas Arvanitoyeorgos
MaRDI profile type: Publication
arXiv ID: 1405.6634
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