From random matrices to stochastic operators
type: Item
instance of: scholarly article
title: From random matrices to stochastic operators
zbMATH Open document ID: 1131.15025
author: Alan Edelman
author: Brian D. Sutton
published in: Journal of Statistical Physics
publication date: 2007-08-20T00:00:00Z
full work available at URL: https://arxiv.org/abs/math-ph/0607038
review text: The authors introduce ideas allowing to interpret classical random matrix models as finite difference schemes for stochastic differential operators. In random matrix theory, three major types of large \(N\) eigenvalue behaviors are described by sine ensembles, Airy ensembles and Bessel ensembles. In this paper, three particular stochastic operators are studied, each associated with one of the above class of local eigenvalue behavior. The stochastic Airy operator displays soft edge behavior associated with the Airy kernel. The stochastic Bessel operator displays hard edge behavior, associated with the Bessel kernel. The article concludes with suggestion for a stochastic sine operator, which would display bulk behavior, associated with the sine kernel.
Mathematics Subject Classification ID: 15B52
Mathematics Subject Classification ID: 65C30
Mathematics Subject Classification ID: 60H10
zbMATH DE Number: 5181145
zbMATH Keywords: local eigenvalue spacing
zbMATH Keywords: finite difference schemes
zbMATH Keywords: stochastic differential operators
zbMATH Keywords: sine ensembles
zbMATH Keywords: Airy ensembles
zbMATH Keywords: Bessel ensembles
reviewed by: Benoit Collins
MaRDI profile type: Publication
OpenAlex ID: W2079474739
arXiv ID: math-ph/0607038
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DOI: 10.1007/S10955-006-9226-4
description: scientific article