On Existence of Cadlag Modification of Coalescing-Fragmentating Wasserstein Dynamics

The discussion will be devoted to a family of interacting particles on the real line which has a connection with the geometry of Wasserstein space of probability measures. We will consider a physical improvement of a classical Howitt-Warren flow (or Arratia flow, in the coalescing case), where particles sticky-reflect (or coalesce) and transfer a mass that influences their motion. We will show that such a model admits a description of each particle by a family of continuous semimartingales which satisfy some natural conditions. We will also discuss some properties of the particle system, in particular, the existence of infinite particle configurations at some moments of time.