Localization for non-stationary Anderson models in three dimensions

TL;DR

This paper establishes localization near the spectrum's bottom for non-stationary Anderson models in three dimensions, utilizing a Wegner estimate, a unique continuation theorem, and combinatorial bounds.

Contribution

It introduces a method to prove localization for non-stationary Anderson models using new estimates and decompositions, extending previous stationary results.

Findings

Proved a Wegner estimate for non-stationary Anderson models

Demonstrated localization near the spectrum's bottom in three dimensions

Utilized a deterministic unique continuation theorem and combinatorial bounds

Abstract

We prove localization (near the bottom of the spectrum) for certain non-stationary variants of the Anderson model in three dimensions. More specifically, we prove a Wegner estimate, which implies localization by existing work. Two key inputs are a deterministic quantitative unique continuation theorem by Li and Zhang [Duke Math. J. 171(2): 327-415, 2022] and some combinatorial decompositions/bounds for non-stationary random potentials proved by the author [Commun. Math. Phys. 407:64, 2026].