Modified Massive Arratia Flow and Wasserstein Diffusion

Abstract

Extending previous work by the first author we present a variant of the Arratia flow, which consists of a collection of coalescing Brownian motions starting from every point of the unit interval. The important new feature of the model is that individual particles carry mass that aggregates upon coalescence and that scales the diffusivity of each particle in an inverse proportional way. In this work we relate the induced measure‐valued process to the Wasserstein diffusion of von Renesse and Sturm. First, we present the process as a martingale solution to an SPDE similar to that of von Renesse and Sturm. Second, as our main result we show a Varadhan formula 42 for short times that is governed by the quadratic Wasserstein distance. © 2018 Wiley Periodicals, Inc.