Spectral properties of the discrete random displacement model

We investigate spectral properties of a discrete random displacement model, a Schrodinger operator on l(2)(Z(d)) with potential generated by randomly displacing finitely supported single-site terms from the points of a sublattice of Z(d). In particular, we characterize the upper and lower edges of the almost sure spectrum. For a one-dimensional model with Bernoulli distributed displacements, we can show that the integrated density of states has a 1/log(2)-singularity at external as well as internal band edges.