Spectral extrema and Lifshitz tails for non monotonous alloy type models

TL;DR

This paper investigates the spectral properties of non-monotonous alloy models, specifically analyzing the ground state energy and Lifshitz tails, where the potential changes sign and the operator's dependence on randomness is non-monotonous.

Contribution

It provides new insights into the spectral behavior of alloy models with sign-changing potentials, extending the understanding of Lifshitz tails in non-monotonous settings.

Findings

Determined the ground state energy for specific non-monotonous alloy models.

Established the existence of Lifshitz tails near the ground state energy.

Analyzed how sign-changing potentials affect spectral properties.

Abstract

In the present note, we determine the ground state energy and study the existence of Lifshitz tails near this energy for some non monotonous alloy type models. Here, non monotonous means that the single site potential coming into the alloy random potential changes sign. In particular, the random operator is not a monotonous function of the random variables.