On the norm of random matrices
type: Item
instance of: scholarly article
title: On the norm of random matrices
zbMATH Open document ID: 0847.15010
author: M. V. Shcherbina
author: Anne Boutet De Monvel
published in: Mathematical Notes
publication date: 1996-05-20T00:00:00Z
review text: It is known that the largest eigenvalue \(\lambda^{(N)}_{\max}\) of the Wigner \(N\times N\) random matrices \(W_N\) converges with probability 1 as \(N\to \infty\) to \(2v\), where \(v^2\) is the variance of the matrix entries [see e.g. \textit{Z. D. Bai} and \textit{Y. Q. Yin}, Ann. Probab. 16, No. 4, 1729-1741 (1988; Zbl 0677.60038)]. The proof concerns analysis of moments \(N^{- 1} \text{Tr } W^k_N\) in asymptotics \(k\), \(N\to \infty\). In the present paper, the moment technique gets its further elegant development. The authors consider random matrix ensembles more general than the Wigner one and obtain large deviations-type statements for respective \(\lambda^{(N)}_{\max}\).
Mathematics Subject Classification ID: 15B52
Mathematics Subject Classification ID: 60H25
Mathematics Subject Classification ID: 60F10
zbMATH DE Number: 857375
zbMATH Keywords: norm
zbMATH Keywords: limiting theorem
zbMATH Keywords: moment method
zbMATH Keywords: Wigner random matrices
zbMATH Keywords: largest eigenvalue
zbMATH Keywords: large deviations
reviewed by: A. Khorunzhy
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 857375