2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/151710We 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 Schrödinger operator at weak disorder.31 pages, 7 eps figures, LaTeX document using AMS symbols (amssym.def, amssym.tex)Disordered Systems and Neural Networkstext