Speaker:  Lorenzo Dello Schiavo (Università di Bonn)

Titolo: The Dirichlet-Ferguson diffusion

Abstract:
We define, via Dirichlet forms’ theory, a geometric diffusion process on the L^2-Wasserstein space over a closed Riemannian manifold. The process is associated with the Dirichlet form induced by the L^2-Wasserstein gradient and by the Dirichlet-Ferguson random measure with intensity the Riemannian volume measure on the base manifold. We discuss the closability of the form via an integration-by-parts formula, which allows explicit computations for the generator and a specification of the process via a measure-valued SPDE. We comment how the construction is related to previous work of von Renesse—Sturm on the Wasserstein Diffusion and of Konarovskyi—von Renesse on the Modified Massive Arratia Flow.