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The fractional Anderson model has been subjectto increasing interest in recent years in the context of materials with anomalous diffusion. I will review some properties and recent results connecting the corresponding Green’s function with the two point function of a self-avoiding walk with long range jumps. These results adapt a strategy proposed by Schenker in 2015and are joint work with Constanza Rojas-Molina and Roberto Maturana Escobar.