Year: 2019
Type: preprint
Abstract: 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 $\partial_t u=\frac{1}{2}Δu -u^2$, 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.
Source: arXiv (Cornell University)
Author: Fan, Wai-Tong Louis
Institution: Indiana University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2968416439