Wegner Estimate for Discrete Alloy-type Models

We study discrete alloy type random Schrödinger operators on `(Z). Wegner estimates are bounds on the average number of eigenvalues in an energy interval of finite box restrictions of these types of operators. If the single site potential is compactly supported and the distribution of the coupling constant is of bounded variation a Wegner estimate holds. The bound is polynomial in the volume of the box and thus applicable as an ingredient for a localisation proof via multiscale analysis. 1. Main results A discrete alloy type model is a family of operators Hω = H0 +Vω on `2(Zd). Here H0 denotes an arbitrary symmetric operator. In most applications H0 is the discrete Laplacian on Zd. The random part Vω is a multiplication operator (1) Vω(x) = ∑