Applied Analysis Seminar Discretization of Diffusions via Gradient Flows

We consider the non-linear Fokker-Planck equation. We show uniform in time bounds for the error of particle approximation in terms of the second Wasserstein distance. We use the variational formulation of non-linear Fokker-Planck and we show that particle approximation can be seen as an inexact gradient flow of free energy functional. To deal with non-local interaction kernel we use results from propagation of chaos theory. The talk will be based on the joint work with Matej Benko, Iwona Chlebicka and Jorgen Endal.