# Asymptotics of the eigenvalues of the Anderson Hamiltonian with white noise potential in two dimensions

## TL;DR

This paper studies the asymptotic behavior of eigenvalues of the two-dimensional Anderson Hamiltonian with white noise potential, showing they grow logarithmically with the domain size and converge to a deterministic constant.

## Contribution

It establishes the almost sure convergence of eigenvalues scaled by log L to a deterministic limit, characterized by a variational formula.

## Key findings

- Eigenvalues divided by log L converge almost surely.
- The limit is a deterministic constant given by a variational formula.
- Provides asymptotic characterization of the spectrum in large domains.

## 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 the eigenvalues divided by $\log L$ converge as $L\rightarrow \infty$ almost surely to the same deterministic constant, which is given by a variational formula.