Anderson Localization for Random Schrödinger Operators with Long Range Interactions

We prove pure point spectrum with exponentially decaying eigenfunctions at all band edges for Schrodinger Operators with a periodic potential plus a random potential of the form V w (x) = Σq i (w)f(x - i), where $f$ decays at infinity like |x|−m for m>4d resp. $m>3d depending on the regularity of f. The random variables q i are supposed to be independent and identically distributed. We assume that their distribution has a bounded density of compact support.