Conservative stochastic PDE and fluctuations of the symmetric simple exclusion process

Understand

In this paper, we provide a continuum model for the fluctuations of the symmetric simple exclusion process about its hydrodynamic limit.

• The model is based on an approximating sequence of stochastic PDEs with nonlinear, conservative noise.
• In the small-noise limit, we show that the fluctuations of the solutions are to first-order the same as the fluctuations of the particle system.
• Furthermore, the SPDEs correctly simulate the rare events in the particle process.