ASYMPTOTICS OF THE EIGENVALUES OF THE ANDERSON HAMILTONIAN WITH WHITE NOISE POTENTIAL IN TWO DIMENSIONS

• 成果类型: Article
• 署名作者: Chouk, Khalil; van Zuijlen, Willem
• 署名单位: University of Edinburgh; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/20-AOP1497
• 发表日期: 2021
• 页码: 1917-1964
• 关键词: model

摘要

In this paper we consider the Anderson Hamiltonian with white noise potential on the box [0, L](2) with Dirichlet boundary conditions. We show that all of the eigenvalues divided by logL, converge as L -> infinity, almost surely to the same deterministic constant which is given by a variational formula.