Decorrelation estimates for the eigenlevels of the discrete Anderson model in the localized regime

TL;DR

This paper establishes decorrelation estimates for eigenvalues of the discrete Anderson model in the localized regime, providing results in one dimension at all energies and in higher dimensions at sufficiently separated energies.

Contribution

It introduces decorrelation estimates for eigenvalues of the Anderson model, extending known results to higher dimensions with energy separation conditions.

Findings

Decorrelation estimates proven for one-dimensional Anderson model at all energies.

In higher dimensions, decorrelation holds for sufficiently separated energies.

Results enhance understanding of eigenvalue behavior in localized regimes.

Abstract

The purpose of the present work is to establish decorrelation estimates for the locally renormalized eigenvalues of the discrete Anderson model near two distinct energies inside the localization region. In dimension one, we prove these estimates at all energies. In higher dimensions, the energies are required to be sufficiently far apart from each other.