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

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 $L\to \mathrm{\infty }$ almost surely to the same deterministic constant, which is given by a variational formula.