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In this expository note we highlight the correlation function method as aunified approach in proving both hydrodynamic limits and fluctuation limits forreaction diffusion particle systems. For simplicity we focus on the case whenthe hydrodynamic limit is $\partial_t u=\frac{1}{2}\Delta u -u^2$, one of thesimplest nonlinear reaction-diffusion equations. The outline of the prooffollows from Chapter 4 of De Masi and Presutti [7] but to simplify thepresentation, we consider reflected Brownian motion instead of reflected randomwalks. We also briefly mention the key ideas in proving the fluctuation result.

Correlation function methods for a system of annihilating Brownian particles