Dynamical localization for the singular Anderson model in Zd

We prove that once one has the ingredients of a “single-energy multiscale analysis result” on the Zd lattice, several spectral and dynamical localization results can be derived, the most prominent being strong dynamical localization (SDL). In particular, given the recent progress at the bottom of the spectrum for the Z2 and Z3 cases with Bernoulli single-site probability distribution, our results imply SDL in these regimes.