Decorrelation estimates for some continuous and discrete random Schr{\"o}dinger operators in dimension one, without covering condition

TL;DR

This paper establishes decorrelation estimates at different energies for one-dimensional random Schrödinger operators, including continuum alloy-type models without covering conditions, aiding in understanding their spectral statistics.

Contribution

It provides the first decorrelation estimates for certain continuum alloy-type models without the covering condition, advancing spectral analysis techniques.

Findings

Decorrelation estimates at distinct energies are proven for specific 1D random Schrödinger operators.

Results apply to continuum alloy-type models without the covering condition.

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{\"o}dinger operator in dimension one. In particular, we establish the result for some random operators on the continuum with alloy-type potential without covering condition assumption. These results are used to give a description of the spectral statistics.