Moderate Deviations for the current and Tagged Particle in Symmetric Simple Exclusion Processes

TL;DR

This paper establishes moderate deviation principles for the position and current of a tagged particle in one-dimensional symmetric simple exclusion processes, providing explicit rate functions based on variational formulas.

Contribution

It introduces explicit expressions for moderate deviation rate functions for tagged particles, building on hydrodynamic limit principles and variational analysis.

Findings

Explicit moderate deviation rate functions derived.

Variational formulas established for tagged particle deviations.

Connections made with hydrodynamic limit principles.

Abstract

We prove moderate deviation principles for the tagged particle position and current in one-dimensional symmetric simple exclusion processes. There is at most one particle per site. A particle jumps to one of its two neighbors at rate $1/2$, and the jump is suppressed if there is already one at the target site. We distinguish one particular particle which is called the tagged particle. We first establish a variational formula for the moderate deviation rate functions of the tagged particle positions based on moderate deviation principles from hydrodynamic limit proved by Gao and Quastel \cite{gao2003moderate}. Then we construct a minimizer of the variational formula and obtain explicit expressions for the moderate deviation rate functions.