Conservative stochastic PDE and fluctuations of the symmetric simple exclusion process

Abstract

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.

arXiv commentThe paper has been entirely rewritten. Our methods now treat the SPDE analogue of the SSEP, including square root noise coefficients, and establish a novel a priori estimate in $L^{\infty }$ for the solutions. We have also added a new section that includes numerical simulations

References in corpus (5)

• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Macroscopic fluctuation theory
• Nonequilibrium Central Limit Theorem for a Tagged Particle in Symmetric Simple Exclusion
• Uniform large deviation principles for Banach space valued stochastic differential equations
• Well-posedness of nonlinear diffusion equations with nonlinear, conservative noise

Cited by in corpus (1)

• Numerical approximation of singular-degenerate parabolic stochastic PDEs