Francesco Saverio Patacchini: Convergence of a particle method for diffusive gradient flows in one dimension

Abstract: We approximate diffusive gradient flows with finite numbers of particles in one dimension. As the quadratic Wasserstein energy is not defined for point-masses, we spread uniformly the mass of each particle in some interval around it. This "tessellation" gives a discrete energy defined on point-masses, which Gamma-converges in the Wasserstein topology to its continuum version as the number of particles increases. Using an abstract result for the convergence of gradient flows in metric spaces by S. Serfaty, we show the convergence of the resulting discrete gradient flow to the continuum one. This is joint work with J. A. Carrillo, Y. Huang, P. Sternberg and G. Wolansky.