Modified Arratia flow and Wasserstein diffusion

An interacting particle system on the real line which is a generalization of the Arratia flow will be considered. We will suppose that particles start from all points of a finite interval, move independently up to the moment of the collision then coalesce and move together. Every particle has a mass influencing on the diffusion and obeying the mass conservation. We will discuss construction of the stochastic flow describing the evolution of such a system as a thermodynamic limit. Also, uniqueness of distribution of such a flow as a solution of a martingale problem, properties of filtration generated by the flow, the large deviation principle and connection with the Wasserstein diffusion will be presented.