On random Schrodinger operators on Z2

This paper is concerned with random lattice operators on Z(2) of the form H-w = Delta + V-w where Delta is the lattice Laplacian and V-w a random potential V-w(n) = w(n)v(n),{w(n)} independent Bernoulli or Gaussian variables and {v(n)} satisfying the condition sup(n) \v(n)\ \n\(rho) < infinity for some rho > 1/2. In this setting and restricting 2 the spectrum away from the edges and 0, existence and completeness of the wave operators is shown. This leads to statements on the a.c. spectrum of H-w. It should be pointed out that, although we do consider here only a specific (and classical) model, the core of our analysis does apply in greater generality.