Gradient flows and particle systems

Stochastic Analysis Seminar Series

Following the groundbreaking work of Jordan-Kinderlehrer-Otto and Benamou-Brenier, a large class of diffusive PDEs can be formulated as gradient flows with respect to some Wasserstein metric. On the other hand many diffusive equations arise as scaling limit of multi-particle systems. In this talk, based  on a joint project with S. Adams, V. Laschos, M. Peletier and J. Zimmer, we explore show that the Wasserstein gradient flow structure can be derived directly from a particle system. This connects the macroscopic entropy (i.e. one among many  Lyapunov functionals) to entropy in a probabilistic sense, thus distinguishing a particular macroscopic entropy-metric pair.


Nicolas Dirr (Cardiff)

Monday, October 22, 2012 - 15:45
to 16:45