Moderate deviations for the facilitated exclusion process in equilibrium

TL;DR

This paper establishes moderate deviation principles for the fluctuation fields of the facilitated exclusion process in equilibrium, utilizing a super-exponential Boltzmann-Gibbs principle based on logarithmic Sobolev inequalities.

Contribution

It introduces a super-exponential Boltzmann-Gibbs principle for the facilitated exclusion process, enabling the derivation of moderate deviation principles in both symmetric and asymmetric cases.

Findings

Moderate deviation principles derived for FEP in equilibrium.

Super-exponential Boltzmann-Gibbs principle proved for FEP.

Applicable to both symmetric and asymmetric FEP.

Abstract

We derive the moderate deviation principles for the fluctuation fields of the facilitated exclusion process (FEP) in one dimension when the process starts from its stationary measure, both in the symmetric and asymmetric cases. The main step is to prove a super-exponential version of the Boltzmann-Gibbs principle, which relies on the logarithmic Sobolev inequality for the FEP.