Moderate deviation principles for a reaction diffusion model in non-equilibrium

TL;DR

This paper establishes moderate deviation principles for a reaction diffusion model combining symmetric exclusion and Glauber dynamics, starting from a non-equilibrium measure, extending understanding of fluctuations in such systems.

Contribution

It proves the moderate deviation principle for the density fluctuation field of a reaction diffusion process starting from a non-equilibrium measure, using a novel lemma.

Findings

Moderate deviation principle established for the model.

Results apply to non-equilibrium initial measures.

Method relies on a key lemma from prior work.

Abstract

We study moderate deviations from hydrodynamic limits of a reaction diffusion model. The process is defined as the superposition of the symmetric exclusion process with a Glauber dynamics. When the process starts from a product measure with a constant density, which is a non-equilibrium measure for the process, we prove that the re-scaled density fluctuation field satisfies the moderate deviation principle. Our proof relies on the so-called main lemma developed by Jara and Menezes in [arXiv:1810.09526, 2018].