Localization near fluctuation boundaries via fractional moments and applications

TL;DR

This paper introduces a novel proof technique for localization in multi-dimensional continuum random Schrödinger operators near fluctuation boundaries, extending fractional moment methods without needing a covering condition, with applications to various random potentials.

Contribution

A new, concise proof of localization properties that broadens the fractional moment method to models without covering conditions, applicable to diverse random potentials.

Findings

Proves localization near fluctuation boundaries in continuum models.

Extends fractional moment method to models without covering conditions.

Includes applications to random surface potentials and displacements.

Abstract

We present a new, short, self-contained proof of localization properties of multi-dimensional continuum random Schr\"odinger operators in the fluctuation boundary regime. Our method is based on the recent extension of the fractional moment method to continuum models in by Aizenman et al, but does not require the random potential to satisfy a covering condition. Applications to random surface potentials and potentials with random displacements are included.