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July 2021 Asymptotics of the eigenvalues of the Anderson Hamiltonian with white noise potential in two dimensions
Khalil Chouk, Willem van Zuijlen
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Ann. Probab. 49(4): 1917-1964 (July 2021). DOI: 10.1214/20-AOP1497

Abstract

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, almost surely to the same deterministic constant which is given by a variational formula.

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Khalil Chouk. Willem van Zuijlen. "Asymptotics of the eigenvalues of the Anderson Hamiltonian with white noise potential in two dimensions." Ann. Probab. 49 (4) 1917 - 1964, July 2021. https://doi.org/10.1214/20-AOP1497

Information

Received: 1 July 2019; Revised: 1 June 2020; Published: July 2021
First available in Project Euclid: 13 May 2021

Digital Object Identifier: 10.1214/20-AOP1497

Subjects:
Primary: 35J10, 35J15, 60F15, 60H25
Secondary: 60F10

Rights: Copyright © 2021 Institute of Mathematical Statistics

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Vol.49 • No. 4 • July 2021
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