Conservative stochastic PDE and fluctuations of the symmetric simple exclusion process

2020/12/03 by Nicolas Dirr, Dirr, Nicolas, Benjamin Fehrman +3 · 3 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2012.02126

openalex publication_date 2020/12/03 · openalex created_date 2020/12/07 · openalex updated_date 2026/07/28

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.

Citations

• Macroscopic fluctuation theory
• Well-posedness of nonlinear diffusion equations with nonlinear,\n conservative noise

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