A hierarchical model for random walks in random media

Abstract

We show that the random walk generated by a hierarchical Laplacian in ℤd has standard diffusive behavior. Moreover, we show that this behavior is stable under a class of random perturbations that resemble an off-diagonal disordered lattice Laplacian. The density of states and its asymptotic behavior around zero energy are computed: singularities appear in one and two dimensions.