Localization for the random displacement model

Frédéric Klopp, Michael Loss, Shu Nakamura, Gunter Stolz

Published 2010-07-15, updated 2011-06-14Version 2

We prove spectral and dynamical localization for the multi-dimensional 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 single-site Neumann problem which can be described as "bubbles tend to the corners".