Moderate deviations for the current and tagged particle in symmetric simple exclusion processes

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 limits proved by Gao and Quastel (2003). Then we construct a minimizer of the variational formula and obtain explicit expressions for the moderate deviation rate functions.