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 $[0,L]^2$ 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.