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May 2021 On fluctuations of global and mesoscopic linear statistics of generalized Wigner matrices
Yiting Li, Yuanyuan Xu
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Bernoulli 27(2): 1057-1076 (May 2021). DOI: 10.3150/20-BEJ1265

Abstract

We consider an N by N real or complex generalized Wigner matrix HN, whose entries are independent centered random variables with uniformly bounded moments. We assume that the variance profile, sij:=E|Hij|2, satisfies i=1Nsij=1, for all 1jN and c1Nsijc for all 1i,jN with some constant c1. We establish Gaussian fluctuations for the linear eigenvalue statistics of HN on global scales, as well as on all mesoscopic scales up to the spectral edges, with the expectation and variance formulated in terms of the variance profile. We subsequently obtain the universal mesoscopic central limit theorems for the linear eigenvalue statistics inside the bulk and at the edges, respectively.

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Yiting Li. Yuanyuan Xu. "On fluctuations of global and mesoscopic linear statistics of generalized Wigner matrices." Bernoulli 27 (2) 1057 - 1076, May 2021. https://doi.org/10.3150/20-BEJ1265

Information

Received: 1 June 2020; Revised: 1 July 2020; Published: May 2021
First available in Project Euclid: 24 March 2021

Digital Object Identifier: 10.3150/20-BEJ1265

Keywords: central limit theorem , generalized Wigner matrix , Linear eigenvalue statistics

Rights: Copyright © 2021 ISI/BS

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Vol.27 • No. 2 • May 2021
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