Localization for the random displacement model at weak disorder

TL;DR

This paper proves Anderson and dynamical localization near the spectrum's bottom for the random displacement model in weak disorder, based on Lifshitz tail and Wegner estimate analysis.

Contribution

It establishes localization results for the model under generic conditions, extending understanding of disordered systems with random displacements.

Findings

Anderson localization near the spectrum's bottom

Dynamical localization in the weak disorder regime

Existence of Lifshitz tail and Wegner estimate for the model

Abstract

This paper is devoted to the study of the random displacement model on $\R^d$. We prove that, in the weak displacement regime, Anderson and dynamical localization holds near the bottom of the spectrum under a generic assumption on the single site potential and a fairly general assumption on the support of the possible displacements. This result follows from the proof of the existence of Lifshitz tail and of a Wegner estimate for the model under scrutiny.