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In this paper, we provide a continuum model for the fluctuations of thesymmetric simple exclusion process about its hydrodynamic limit. The model isbased on an approximating sequence of stochastic PDEs with nonlinear,conservative noise. In the small-noise limit, we show that the fluctuations ofthe solutions are to first-order the same as the fluctuations of the particlesystem. Furthermore, the SPDEs correctly simulate the rare events in theparticle process. We prove that the solutions satisfy a zero-noise largedeviations principle with rate function equal to the rate function describingthe deviations of the symmetric simple exclusion process from its hydrodynamiclimit.

Conservative stochastic PDE and fluctuations of the symmetric simple exclusion process