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

Abstract

In this paper we consider the Anderson Hamiltonian with white noise potential on the box ${[0,\mathit{L}]}^2$ with Dirichlet boundary conditions. We show that all of the eigenvalues divided by $log\mathit{L}$, converge as $\mathit{L}\to \infty$, almost surely to the same deterministic constant which is given by a variational formula.