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Quasi-potential for the one dimensional SSEP in weak contact with reservoirs

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  • Landim, Claudio
  • Velasco, Sonia

Abstract

We derive a formula for the quasi-potential of the one-dimensional symmetric exclusion process in weak contact with reservoirs. The interaction with the boundary is so weak that, in the diffusive scale, the density profile evolves as the one of the exclusion process with reflecting boundary conditions. In order to observe an evolution of the total mass, the process has to be observed in a longer time-scale, in which the density profile becomes immediately constant.

Suggested Citation

  • Landim, Claudio & Velasco, Sonia, 2024. "Quasi-potential for the one dimensional SSEP in weak contact with reservoirs," Stochastic Processes and their Applications, Elsevier, vol. 177(C).
    • Handle: RePEc:eee:spapps:v:177:y:2024:i:c:s0304414924001509
    DOI: 10.1016/j.spa.2024.104444
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    References listed on IDEAS

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    1. Bodineau, Thierry & Giacomin, Giambattista, 2004. "From dynamic to static large deviations in boundary driven exclusion particle systems," Stochastic Processes and their Applications, Elsevier, vol. 110(1), pages 67-81, March.
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