Expansion of the spectrum in the weak disorder regime for random operators in continuum space

TL;DR

This paper investigates how the spectrum of random ergodic Schrödinger-type operators expands at the bottom in the weak disorder regime, providing bounds for general perturbations of a periodic elliptic operator.

Contribution

It offers new bounds on spectral expansion in the weak disorder regime for a broad class of background operators, including higher-order elliptic operators.

Findings

Bounds on spectrum expansion at the bottom for weak disorder

Applicable to general perturbations of periodic elliptic operators

Extends understanding beyond second-order operators

Abstract

We study the spectrum of random ergodic Schroedinger-type operators in the weak disorder regime. We give upper and lower bounds on how much the spectrum expands at its bottom for very general perturbations. The background operator is assumed to be a periodic elliptic differential operator on R^d, not necessarily of second order.