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

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

Stochastic Processes and their Applications, 2020, vol. 130, issue 7, 4326-4357

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.

Date: 2020
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DOI: 10.1016/j.spa.2019.12.006

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