We investigate spectral properties of a discrete random displacement model, a Schrödinger operator on l2(ℤd) with potential generated by randomly displacing finitely supported single-site terms from the points of a sublattice of ℤd. 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/log2-singularity at external as well as internal band edges.
