Limits of spectral measures for linearly bounded and for Poisson distributed random potentials

TL;DR

This paper establishes the existence of infinite volume limits for spectral measures of certain Schroedinger operators, including those with Poisson distributed random potentials, advancing understanding of their spectral properties.

Contribution

It proves the existence of infinite volume limits of resolvents and spectral measures for linearly bounded and Poisson random potentials, extending spectral theory results.

Findings

Existence of infinite volume limits for spectral measures

Application to Poisson distributed random potentials

Advancement in spectral analysis of random Schroedinger operators

Abstract

We show the existence of infinite volume limits of resolvents and spectral measures for a class of Schroedinger operators with linearly bounded potentials. We then apply this result to Schroedinger operators with a Poisson distributed random potential.