Anderson Localization Induced by Random Defects of a Ragged Boundary

We study alloy-type Anderson Hamiltonians in finite-width layers in Euclidean spaces and in periodic lattices of arbitrary dimension. The disorder is induced by random microscopic defects of the boundary carrying extra potentials of infinite range featuring a power-law decay. We consider two extreme cases of disorder: with most singular, Bernoulli probability distributions, and with very regular ones, admitting a bounded probability density. Exponential spectral and sub-exponential dynamical localization are proved in both cases, by extending the methods of our papers [6, 7] from IID to correlated (Markov) random fields generating the disorder. In the smooth disorder case, we prove an asymptotically exponential strong dynamical localization under the optimal condition on the decay rate of the local potentials (summability).