We prove spectral and dynamical localization for the multidimensional random displacement model near the bottom of its spectrum by showing that the approach through multiscale analysis is applicable. In particular, we show that a previously known Lifshitz tail bound can be extended to our setting and prove a new Wegner estimate. A key tool is given by a quantitative form of a property of a related singlesite Neumann problem which can be described as "bubbles tend to the corners.". © 2012.
