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

被引：12

作者：

Chouk, Khalil ^{[1
]}

van Zuijlen, Willem ^{[2
]}

机构：

[1] Univ Edinburgh, Sch Math, Edinburgh, Midlothian, Scotland

[2] Weierstrass Inst Appl Anal & Stochast, Berlin, Germany

来源：

ANNALS OF PROBABILITY | 2021年 / 49卷 / 04期

基金：

欧洲研究理事会;

关键词：

Anderson Hamiltonian; white noise; paracontrolled distributions; operators with Dirichlet boundary conditions; MODEL;

D O I：

10.1214/20-AOP1497

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

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.

引用

页码：1917 / 1964

页数：48

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