Asymptotic ergodicity of the eigenvalues of random operators in the localized phase
type: Item
instance of: scholarly article
title: Asymptotic ergodicity of the eigenvalues of random operators in the localized phase
zbMATH Open document ID: 1281.82014
author: Frédéric Klopp
publication date: 2013-05-13T00:00:00Z
full work available at URL: https://arxiv.org/abs/1012.0831
review text: From the author's abstract: The author proves that, for a general class of random operators, the family of the unfolded eigenvalues in the localization region is asymptotically ergodic in the sense of \textit{N. Minami} [Special issue: Spectra of random operators and related topics. RIMS Kôkyûroku Bessatsu B27, 169 p. (2011; Zbl 1255.60004)]. Minami conjectured this to be the case for the discrete Anderson model in the localized regime. The author also provides a local analogue of this result. From the asymptotic ergodicity, one can recover the statistics of the level spacings as well as a number of other spectral statistics. The proof relies on the analysis developed by \textit{F. Germinet} and \textit{F. Klopp} [RIMS Kôkyûroku Bessatsu B27, 11--24 (2011; Zbl 1234.81075)].
reviewed by: Julien Poisat
Mathematics Subject Classification ID: 82B44
Mathematics Subject Classification ID: 47B80
Mathematics Subject Classification ID: 60H25
zbMATH DE Number: 6162377
zbMATH Keywords: random operators
zbMATH Keywords: localization
zbMATH Keywords: eigenvalues
zbMATH Keywords: asymptotic ergodicity
zbMATH Keywords: discrete Anderson model
MaRDI profile type: Publication
OpenAlex ID: W2964174226
arXiv ID: 1012.0831
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DOI: 10.1007/S00440-012-0415-6
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article