Location
MC 5501
Speaker
Nicolas Perkowski, Free University of Berlin
Title
Mesoscopic approximation of nonequilibrium particle systems
Abstract
Effective descriptions of large systems of interacting particles on mesoscopic scales typically lead to stochastic PDEs driven by space-time white noise. In non-equilibrium systems, these equations are nonlinear, singular SPDEs. The interplay of very rough noise and nonlinearity makes classical theories breaks down and may require renormalization. In my talk I will discuss how these singular equations formally arise, and the difficulties and methods for solving them. Two emblematic examples are the Dean-Kawasaki equation, modeling mesoscopic density fluctuations in mean-field particle systems, and the KPZ/Burgers equation, describing interface growth fluctuations. I will discuss quantitative approximation results for them based on new regularity estimates for the associated infinite-dimensional Kolmogorov equations. Based on joint works with Ana Djurdjevac, Lukas Gräfner, Helena Kremp and Xiaohao Ji.