Some trace monotonicity properties and applications

TL;DR

This paper investigates trace monotonicity properties of functions of self-adjoint operators and applies these findings to prove a key estimate in random Schrödinger operator models.

Contribution

It introduces new trace monotonicity results and completes the proof of the Wegner estimate for continuum random Schrödinger operators.

Findings

Established trace monotonicity properties for functions of self-adjoint operators

Applied results to complete the Wegner estimate proof

Enhanced understanding of spectral properties in random Schrödinger models

Abstract

We present some results on the monotonicity of some traces involving functions of self-adjoint operators with respect to the natural ordering of their associated quadratic forms. We also apply these results to complete a proof of the Wegner estimate for continuum models of random Schr\"odinger operators as given in \cite{co-hi1}.