An uncertainty principle, Wegner estimates and localization near fluctuation boundaries

TL;DR

This paper establishes an uncertainty principle and applies it to derive Wegner estimates near fluctuation boundaries, enabling the proof of localization at low energies for new classes of models.

Contribution

It introduces a simple uncertainty principle and demonstrates its application to prove Wegner estimates near fluctuation boundaries, advancing localization theory.

Findings

Proved a new uncertainty principle.

Derived Wegner estimates near fluctuation boundaries.

Established localization at low energies for new models.

Abstract

We prove a simple uncertainty principle and show that it can be applied to prove Wegner estimates near fluctuation boundaries. This gives new classes of models for which localization at low energies can be proven.