  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
cut-off. This leads to an asymptotic expansion for the density of states. We
believe this is an important first step towards a rigourous analysis of the
density of states in the free spectrum of a random Schr\"odinger operator at
weak disorder.
