Random matrix theory has been proved to be a successful tool in the study of some complex quantum systems. In this talk we will consider a random band matrix W-orbital model, which models the behaviour of an electron in a lattice of metallic grains. Our goal will be to obtain an asymptotic expression in W for the averaged density of states of the system. To this end we will introduce the so-called Grassmann variables and obtain expressions which are uniform in the size of the lattice using a cluster expansion.
