Poisson-type limit theorems for eigenvalues of finite-volume Anderson Hamiltonians

Abstract

We consider the spectral problem for the random Schrodinger operator on the multidimensional lattice torus increasing to the whole of lattice, with an i.i.d. potential (Anderson Hamiltonian). We prove complete Poisson-type limit theorems for the (normalized) eigenvalues and their locations, provided that the upper tails of the distribution of potential decay at infinity slower than the double exponential tails. For the fractional-exponential tails, the strong influence of the parameters of the model on a specification of the normalizing constants is described.