Large deviations for conservative stochastic PDE and non-equilibrium fluctuations

摘要: The large deviations rate function for nonlinear diffusion equations with conservative, white noise is identified by proving the $\Gamma$-convergence of functions to approximating stochastic PDE. In addition, a corresponding uniform principle joint small noise, ultra-violet cutoff limit SPDE obtained. limiting shown coincide describing zero range process from its hydrodynamic limit. proof relies on detailed analysis associated skeleton equation---a degenerate parabolic-hyperbolic PDE irregular drift. well-posedness and stability this class in energy-critical spaces second main result work.