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arXiv · 2203.05260

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

Xiaofeng Xue·Linjie Zhao
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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.

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Xiaofeng Xue, Linjie Zhao. 2022-03-10. Moderate Deviations for the current and Tagged Particle in Symmetric Simple Exclusion Processes. https://arxiv.org/abs/2203.05260

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