Decorrelation estimates for a 1D tight binding model in the localized regime

TL;DR

This paper proves decorrelation estimates for eigenvalues of a 1D tight binding model in the localized regime, demonstrating asymptotic independence of local level statistics near multiple energies.

Contribution

It introduces new decorrelation estimates for eigenvalues in a 1D tight binding model, enabling analysis of local level statistics at multiple energies.

Findings

Eigenvalues exhibit decorrelation near distinct energies in the localized regime

Asymptotic independence of local level statistics is established for multiple energies

Results apply to arbitrary fixed number of energies n

Abstract

In this article, we prove decorrelation estimates for the eigenvalues of a 1D discrete tight binding model near two distinct energies in the localized regime. Consequently, with an arbitrary, fixed number n, the asymptotic independence for local level statistics near n distinct energies is obtained.