  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.
