Localization in general one dimensional random systems. I: Jacobi matrices
type: Item
instance of: scholarly article
title: Localization in general one dimensional random systems. I: Jacobi matrices
zbMATH Open document ID: 0604.60062
DOI: 10.1007/BF01229383
published in: Communications in Mathematical Physics
publication date: 1985-01-01T00:00:00Z
review text: We consider random discrete Schrödinger operators in a strip with a potential \(V_{\omega}(n,\alpha)\) (n a label in \({\mathbb{Z}}\) and \(\alpha\) a finite label ''across'' the strip) and \(V_{\omega}\) an ergodic process. We prove that \(H_ 0+V_{\omega}\) has only point spectrum with probability one under two assumptions: (1) The conditional distribution of \(\{V_{\omega}(n,\alpha)\}_{n=0,1;all\quad \alpha}\) conditioned on \(\{V_{\omega}\}_{n\neq 0,1;all\quad \alpha}\) has an absolutely continuous component with positive probability. (2) For a.e. E, no Lyapunov exponent is zero.
Mathematics Subject Classification ID: 60H25
Mathematics Subject Classification ID: 81P20
zbMATH DE Number: 3976028
zbMATH Keywords: random discrete Schrödinger operators
zbMATH Keywords: Lyapunov exponent
author: B. Simon
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01229383
OpenAlex ID: W2092804045
description: scientific article; zbMATH DE number 3976028