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One of the fundamental results in the theory of localization for discreteSchr\"odinger operators with random potentials is the exponential decay ofGreen's function and the absence of continuous spectrum. In this paper weprovide a new variant of these results for one-dimensional alloy-typepotentials with finitely supported sign-changing single-site potentials usingthe fractional moment method.

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