Decorrelation estimates for some continuous and discrete random schr\"odinger operators in dimension one and applications to spectral statistics

TL;DR

This paper establishes decorrelation estimates at different energies for one-dimensional random Schrödinger operators, including continuum alloy-type models, and applies these results to analyze spectral statistics.

Contribution

It provides new decorrelation estimates for certain one-dimensional random Schrödinger operators, enhancing understanding of their spectral statistics.

Findings

Decorrelation estimates at distinct energies are proven for specific models.

Results apply to continuum alloy-type potentials.

Spectral statistics are characterized using these decorrelation estimates.

Abstract

The purpose of the present work is to establish decorrelation estimates at distinct energies for some random Schr\"odinger operator in dimension one. In particular, we establish the result for some random operators on the continuum with alloy-type potential. These results are used to give a description of the spectral statistics.