Abstract:
In this talk, which is based on joint work with Benjamin Gess, we will draw the link between large deviations in interacting particle systems and large deviations for certain classes of stochastic PDE. The motivating example will be the large deviations of the zero range process about its hydrodynamic limit. We will show informally that the corresponding rate function is identical to the rate function appearing for a degenerate stochastic PDE with nonlinear, conservative noise. Our primary result is a rigorous proof of this fact based upon an intricate treatment of the corresponding skeleton PDE, which is a nonlinear, energy-critical advection-diffusion equation.