A particle model for Wasserstein type diffusion

In the talk we will present an interacting particle model on the real line which has a connection with the geometry of Wasserstein space. The model is a natural generalization of the coalescing Brownian motions but now particles can sticky-reflected from each other. The fundamental new feature is that particles carry mass which is aggregated as more and more particles occupy the same position and which determines the diffusivity of the individual particle in inverse proportional way. We are going to present the infinite dimensional SDE with discontinuous coefficients which describes the particle model. We will discuss the existence of a weak solution such an equation, using a finite particle approximation. Also the stationary case will be considered and an invariant measure will be constructed. Joint work with Max von Renesse.