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
收藏
页码：1917 / 1964
页数：48
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