Precise asymptotics for beta ensembles
type: Item
instance of: scholarly article
title: Precise asymptotics for beta ensembles
zbMATH Open document ID: 1276.15020
author: Xingyuan Zeng
author: Zhenting Hou
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 2013-08-09T00:00:00Z
review text: The edge properties of the spectrum of random matrices are investigated. The paper extends results by \textit{Z. Su} [Acta Math. Sin., Engl. Ser. 24, No. 6, 971--982 (2008; Zbl 1154.60034)]) who first obtained precise asymptotic results for the largest eigenvalues of the Gaussian unitary ensemble and of the Laguerre unitary ensemble for \(\beta = 2\). The new results are obtained for both the largest eigenvalues and the smallest eigenvalues of the \(\beta\)-Hermite and \(\beta\)-Laguerre ensembles using the general \(\beta\) Tracy-Widom law together with the results for small deviation inequalities for random matrices in the paper by \textit{M. Ledoux} and \textit{B. Rider} [Electron. J. Probab. 15, 1319--1343 (2010; Zbl 1228.60015)].
Mathematics Subject Classification ID: 15B52
Mathematics Subject Classification ID: 60B20
Mathematics Subject Classification ID: 15A42
zbMATH DE Number: 6197292
zbMATH Keywords: extremal eigenvalues
zbMATH Keywords: \(\beta\)-ensembles
zbMATH Keywords: general \(\beta\) Tracy-Widom law
zbMATH Keywords: small deviation inequalities
zbMATH Keywords: random matrices
zbMATH Keywords: Gaussian unitary ensemble
zbMATH Keywords: Laguerre unitary ensemble
MaRDI profile type: Publication
full work available at URL: s13226-013-0020-0
OpenAlex ID: W2086765642
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DOI: 10.1007/S13226-013-0020-0
description: scientific article; zbMATH DE number 6197292