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Conservative stochastic PDE and fluctuations of the symmetric simple exclusion process

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arxiv 2012.02126 v2 pith:NPH6A7Y2 submitted 2020-12-03 math.PR math.AP

Nicolas Dirr , Benjamin Fehrman , Benjamin Gess This is my paper · ORCID
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keywords fluctuationsprocessexclusionlimitsimplesymmetricconservativedeviations
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In this paper, we provide a continuum model for the fluctuations of the symmetric simple exclusion process about its hydrodynamic limit. The model is based on an approximating sequence of stochastic PDEs with nonlinear, conservative noise. In the small-noise limit, we show that the fluctuations of the solutions are to first-order the same as the fluctuations of the particle system. Furthermore, the SPDEs correctly simulate the rare events in the particle process. We prove that the solutions satisfy a zero-noise large deviations principle with rate function equal to the rate function describing the deviations of the symmetric simple exclusion process from its hydrodynamic limit.

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Cited by 4 Pith papers

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