Localization via fractional moments for models on {\bb Z} with single-site potentials of finite support

One of the fundamental results in the theory of localization for discrete Schrödinger operators with random potentials is the exponential decay of Green's function and the absence of a continuous spectrum. In this paper, we provide a new variant of these results for one-dimensional alloy-type potentials with finitely supported sign-changing single-site potentials using the fractional moment method.

Dedicated to the memory of Pierre Duclos.