Monotonicity properties of exclusion sensitivity

TL;DR

This paper investigates how the properties of exclusion sensitivity and stability in symmetric exclusion processes on graphs change when edges are added, focusing on monotonicity and spectral analysis of the process generator.

Contribution

It provides insights into the monotonicity of exclusion sensitivity and stability with respect to graph edge addition, using spectral analysis of the process generator.

Findings

Eigenvector and eigenvalue analysis of the process generator on complete graphs

Results on how adding edges affects exclusion sensitivity and stability

Answers to specific questions about monotonicity properties

Abstract

In~\cite{bgs2013}, exclusion sensitivity and exclusion stability for symmetric exclusion processes on graphs were defined as a natural analogue of noise sensitivity and noise stability in this setting. As these concepts were defined for any sequence of connected graphs, it is natural to study the monotonicity properties of these definitions with respect to adding edges to the graphs, and in particular, whether some graphs are more stable or sensitive than others. The main purpose of this paper is to answer some such question from~\cite{bgs2013}. The main tool used is included results about the eigenvectors and eigenvalues of the generator of symmetric exclusion processes on complete graphs.