A large deviation principle for Wigner matrices without Gaussian tails
type: Item
instance of: scholarly article
title: A large deviation principle for Wigner matrices without Gaussian tails
zbMATH Open document ID: 1330.60012
DOI: 10.1214/13-AOP866
author: Charles Bordenave
author: Pietro Caputo
published in: The Annals of Probability
publication date: 2014-11-14T00:00:00Z
full work available at URL: https://arxiv.org/abs/1207.5570
review text: Let \(H\) be an \(n \times n\) square Hermitian matrix with i.i.d.\ entries with tail \(P(|H_{ij}|>t) \leq \exp(-a t^b)\) with \(a>0\) and \(1<b<2\). The main result is a large deviations principle for the empirical spectral distribution of \(H/\sqrt{n}\) with speed \(n^{1+b/2}\) and good rate function related to the free divisibility with respect to the semicircle law. The proof is based on a clever additive decomposition of the matrix. This is to date the unique example of a large deviations principle for the empirical spectral distribution of a nonunitary invariant ensemble of random matrices.
reviewed by: Djalil Chafaï
Mathematics Subject Classification ID: 60B20
Mathematics Subject Classification ID: 15B52
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 15A18
zbMATH DE Number: 6369480
zbMATH Keywords: random matrices
zbMATH Keywords: spectral measure
zbMATH Keywords: large deviations
zbMATH Keywords: free convolution
zbMATH Keywords: random networks
zbMATH Keywords: local weak convergence
MaRDI profile type: Publication
arXiv ID: 1207.5570
description: scientific article; zbMATH DE number 6369480