Initial length scale estimate for waveguides with some random singular potentials

TL;DR

This paper establishes initial length scale estimates for multi-dimensional waveguides affected by various types of random singular potentials, including large measure-supported, oscillating, and delta potentials, advancing understanding of their spectral properties.

Contribution

It provides the first initial length scale estimates for waveguides with three types of random singular perturbations, broadening the theoretical framework for such models.

Findings

Proved initial length scale estimate for large measure-supported potentials

Established estimates for fast oscillating potentials

Analyzed delta-potential perturbations in waveguides

Abstract

In this work we consider three examples of random singular perturbations in multi-dimensional models of waveguides. These perturbations are described by a large potential supported on a set of a small measure, by a compactly supported fast oscillating potential, and by a delta-potential. In all cases we prove initial length scale estimate.