2019/08/15 by Wai-Tong Louis Fan, Fan, Wai-Tong Louis
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Diffusion and Search Dynamics #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Methodology (stat.ME) #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1908.05654
openalex publication_date 2019/08/15 · openalex created_date 2019/08/22 · openalex updated_date 2026/07/28
In this expository note we highlight the correlation function method as a unified approach in proving both hydrodynamic limits and fluctuation limits for reaction diffusion particle systems. For simplicity we focus on the case when the hydrodynamic limit is ∂t u=(1)/(2)Δu -u2, one of the simplest nonlinear reaction-diffusion equations. The outline of the proof follows from Chapter 4 of De Masi and Presutti [7] but to simplify the presentation, we consider reflected Brownian motion instead of reflected random walks. We also briefly mention the key ideas in proving the fluctuation result.