Mean Green ’ s function of the Anderson model at weak disorder with an infra - red cut - off

In this paper we develop a polymer expansion with large/small field conditions for the mean resolvent of a weakly disordered system. Then we show that we can apply our result to a two-dimensional model, for energies outside the unperturbed spectrum or in the free spectrum provided the potential has an infra-red cutoff. This leads to an asymptotic expansion for the density of states. We believe this is an important first step towards a rigorous analysis of the density of states in the free spectrum of a random Schrödinger operator at weak disorder.