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

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  • Xue, Xiaofeng
  • Zhao, Linjie

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.

Suggested Citation

  • Xue, Xiaofeng & Zhao, Linjie, 2024. "Moderate deviations for the current and tagged particle in symmetric simple exclusion processes," Stochastic Processes and their Applications, Elsevier, vol. 167(C).
    • Handle: RePEc:eee:spapps:v:167:y:2024:i:c:s0304414923001825
    DOI: 10.1016/j.spa.2023.09.005
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    References listed on IDEAS

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    1. Puhalskii, A., 1994. "The method of stochastic exponentials for large deviations," Stochastic Processes and their Applications, Elsevier, vol. 54(1), pages 45-70, November.
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