Equilibrium moderate deviations for occupation times of SSEP on regula trees

TL;DR

This paper establishes moderate deviation principles for occupation times of the symmetric simple exclusion process on regular trees, using duality and replacement lemmas to analyze the process starting from an invariant measure.

Contribution

It introduces new moderate deviation results for occupation times of SSEP on regular trees, employing duality and novel replacement lemmas.

Findings

Moderate deviation principles for occupation times are proven.

Duality relationships are effectively used to derive key lemmas.

The results apply to the symmetric exclusion process on regular trees.

Abstract

In this paper, we are concerned with the symmetric simple exclusion process on the regula tree $\mathbb{T}^d$ for $d\geq 2$. Our main result gives moderate deviation principles of occupation times of the process starting from an invariant product measure. Two replacement lemmas play key roles in the proof of our main result. To obtain these replacement lemmas, we utilize duality relationships between the symmetric exclusion process and two types of random walks on $\mathbb{T}^d$ and $\left(\mathbb{T}^d\right)^2$ respectively.