Level spacing and Poisson statistics for continuum random Schrödinger operators
type: Item
instance of: scholarly article
title: Level spacing and Poisson statistics for continuum random Schrödinger operators
zbMATH Open document ID: 1467.82037
DOI: 10.4171/JEMS/1033
author: Yanyan Li
published in: Journal of the European Mathematical Society (JEMS)
publication date: 2021-06-10T00:00:00Z
review text: Summary: We prove a probabilistic level-spacing estimate at the bottom of the spectrum for continuum alloy-type random Schrödinger operators, assuming sign-definiteness of a single-site bump function and absolutely continuous randomness. More precisely, given a finite-volume restriction of the random operator onto a box of linear size \(L\), we prove that with high probability the eigenvalues below some threshold energy \(E_{\mathrm{sp}}\) keep a distance of at least \(e^{-\log L)^\beta}\) for sufficiently large \(\beta>1\). This implies simplicity of the spectrum of the infinite-volume operator below \(E_{\mathrm{sp}}\). Under the additional assumption of Lipschitz-continuity of the single-site probability density we also prove a Minami-type estimate and Poisson statistics for the point process given by the unfolded eigenvalues around a reference energy \(E\).
Mathematics Subject Classification ID: 82B44
Mathematics Subject Classification ID: 47B80
Mathematics Subject Classification ID: 60H25
zbMATH DE Number: 7357349
zbMATH Keywords: Anderson localization
zbMATH Keywords: Poisson statistics of eigenvalues
zbMATH Keywords: Minami estimate
zbMATH Keywords: level statistics
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.4171/jems/1033
OpenAlex ID: W3115844419
description: scientific article; zbMATH DE number 7357349