Reversible Coalescing-Fragmentating Wasserstein Dynamics on the Real Line

The talk is devoted to a model of interacting diffusion particles on the real line. We propose a family of reversible fragmentating-coagulating processes of particles of varying size-scaled diffusivity with strictly local interaction. The construction is based on a new family of measures on the set of real increasing functions as reference measures for naturally associated Dirichlet forms. The processes are infinite dimensional versions of sticky reflecting dynamics on a simplex. We also identify the intrinsic metric leading to a Varadhan formula for the short time asymptotics with the Wasserstein metric for the associated measure valued diffusion. Joint work with Max von Renesse.