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

Xiaofeng Xue and Linjie Zhao

Stochastic Processes and their Applications, 2024, vol. 167, issue C

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.

Keywords: Moderate deviation; Tagged particle; Current; Exclusion process (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spa.2023.09.005

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