Speaker
Description
It is well known that the hydrodynamic limit of several classes of stochastic interacting particle systems is described by nonlinear Fokker–Planck equations with local interactions. This is the case, for example, for basic stochastic lattice gas models such as the zero-range process and the simple exclusion process. The aim of this talk is to introduce a simple probabilistic approach that allows one to establish exponential convergence to equilibrium in Wasserstein distance for the PDEs describing the hydrodynamic limit of lattice gases. This approach blends together coupling techniques with the monotonicity property of both the interaction coefficients and the underlying particle system. As such, it offers an alternative to generalized McCann’s conditions and entropy methods, and it naturally adapts to the presence of non-convex transport terms in the dynamics.