Correlation function methods for a system of annihilating Brownian particles

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.

arXiv comment9 pages expository note

References in corpus (2)

• Derivation of the Cubic Non-linear Schrödinger Equation from Quantum Dynamics of Many-Body Systems
• Systems of interacting diffusions with partial annihilation through membranes