English

Localization for the random displacement model

Mathematical Physics 2019-12-19 v2 math.MP Spectral Theory

Abstract

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".

Keywords

Cite

@article{arxiv.1007.2483,
  title  = {Localization for the random displacement model},
  author = {Frédéric Klopp and Michael Loss and Shu Nakamura and Gunter Stolz},
  journal= {arXiv preprint arXiv:1007.2483},
  year   = {2019}
}

Comments

Corrected typos and improved some arguments

R2 v1 2026-06-21T15:48:19.585Z