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Correlation function methods for a system of annihilating Brownian particles
- Publication Year :
- 2019
-
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 $\partial_t u=\frac{1}{2}\Delta u -u^2$, 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.<br />Comment: 9 pages expository note
- Subjects :
- Mathematics - Probability
Mathematical Physics
Statistics - Methodology
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1908.05654
- Document Type :
- Working Paper