Universality of the local spacing distribution in certain ensembles of Hermitian Wigner matrices
type: Item
instance of: scholarly article
title: Universality of the local spacing distribution in certain ensembles of Hermitian Wigner matrices
zbMATH Open document ID: 0978.15020
author: Kurt Johansson
published in: Communications in Mathematical Physics
publication date: 2001-08-09T00:00:00Z
full work available at URL: https://arxiv.org/abs/math-ph/0006020
review text: The author considers the distribution of the distances between adjacent eigenvalues for Hermitian random matrices with independent entries. It is conjectured that this generally is the same as with the Gaussian unitary ensemble. Theorem 1.3 shows this is true for a class \(W^p_a\) involving convolutions of a fixed Gaussian density with a distribution having finite moments, fixed variance and varying with the different entries. Results on Brownian motion are used in the proof.
reviewed by: Ki Hang Kim
Mathematics Subject Classification ID: 15B52
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 15A18
zbMATH DE Number: 1631876
zbMATH Keywords: eigenvalues of random matrix
zbMATH Keywords: Hermitian Wigner matrix
zbMATH Keywords: Gaussian unitary ensemble
zbMATH Keywords: Brownian motion
zbMATH Keywords: local spacing distribution
MaRDI profile type: Publication
OpenAlex ID: W1968062933
arXiv ID: math-ph/0006020
DOI: 10.1007/S002200000328
description: scientific article; zbMATH DE number 1631876