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.
Keywords
Cite
@article{arxiv.2012.02126,
title = {Conservative stochastic PDE and fluctuations of the symmetric simple exclusion process},
author = {Nicolas Dirr and Benjamin Fehrman and Benjamin Gess},
journal= {arXiv preprint arXiv:2012.02126},
year = {2024}
}
Comments
The 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