Probability Seminar: Particle Approximation of the Wasserstein Diffusion

In this talk a finite dimensional approximation of the recently constructed Wasserstein diffusion on the unit interval is presented. More precisely, the empirical measure process associated to a system of interacting, two-sided Bessel processes with dimension $0 < \delta < 1$ converges in distribution to the Wasserstein diffusion under the equilibrium fluctuation scaling. The passage to the limit is based on Mosco convergence of the associated Dirichlet forms in the generalized sense of Kuwae/Shioya. This is joint work with Max von Renesse.