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Non-equilibrium and stationary fluctuations for the SSEP with slow boundary

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  • Gonçalves, P.
  • Jara, M.
  • Menezes, O.
  • Neumann, A.

Abstract

We derive the non-equilibrium fluctuations of one-dimensional symmetric simple exclusion processes in contact with stochastic reservoirs which are regulated by a factor n−θ. Depending on the range of θ we obtain processes with various boundary conditions. Moreover, as a consequence of the previous result, we deduce the non-equilibrium stationary fluctuations.The main ingredient to prove these results is the derivation of precise bounds on the two-point space–time correlation function, which are a consequence of precise bounds on the transition probabilities of some underlying random walks.

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  • Gonçalves, P. & Jara, M. & Menezes, O. & Neumann, A., 2020. "Non-equilibrium and stationary fluctuations for the SSEP with slow boundary," Stochastic Processes and their Applications, Elsevier, vol. 130(7), pages 4326-4357.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:7:p:4326-4357
    DOI: 10.1016/j.spa.2019.12.006
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    1. Franco, Tertuliano & Gonçalves, Patrícia & Neumann, Adriana, 2019. "Non-equilibrium and stationary fluctuations of a slowed boundary symmetric exclusion," Stochastic Processes and their Applications, Elsevier, vol. 129(4), pages 1413-1442.
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    Cited by:

    1. Zhao, Linjie, 2022. "Long-time behavior of SSEP with slow boundary," Statistics & Probability Letters, Elsevier, vol. 185(C).

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    1. Zhao, Linjie, 2022. "Long-time behavior of SSEP with slow boundary," Statistics & Probability Letters, Elsevier, vol. 185(C).

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