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Erhard, D.; Franco, T.; Gonçalves, P.; Neumann, A.; Tavares, M.

Non-equilibrium fluctuations for the SSEP with a slow bond. (English. French summary) Zbl 1434.60286

Ann. Inst. Henri Poincaré, Probab. Stat. 56, No. 2, 1099-1128 (2020).
Summary: We prove the non-equilibrium fluctuations for the one-dimensional symmetric simple exclusion process with a slow bond. This generalizes a result of our former work [Stochastic Processes Appl. 123, No. 12, 4156–4185 (2013; Zbl 1296.60261)], which dealt with the equilibrium fluctuations. The foundation stone of our proof is a precise estimate on the correlations of the system, and that is by itself one of the main novelties of this paper. To obtain these estimates, we first deduce a spatially discrete PDE for the covariance function and we relate it to the local times of a random walk in a non-homogeneous environment via Duhamel’s principle. Projection techniques and coupling arguments reduce the analysis to the problem of studying the local times of the classical random walk. We think that the method developed here can be applied to a variety of models, and we provide a discussion on this matter.

Cited in 5 Documents

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory

Keywords:

non-equilibrium fluctuations; slowed exclusion; local times of random walks; two point correlation function

Citations:

Zbl 1296.60261
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Full Text: DOI arXiv Euclid

References:

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