On Some Annihilating and Coalescing Systems

In the present paper we continue the investigation of the so-called coalescing ideal gas in one dimension, initiated by Ermakov. The model consists of point-like particles moving with velocities ±1 which coalesce and choose a fresh velocity with the same distribution when colliding. In the previous paper various identities in law were derived for the infinitely extended system. In the present paper we consider the scaling limit of the model in its various guises. The main result is the derivation of the scaling limit (invariance principle) for the joint law of an arbitrary finite number of individual particle trajectories in this system. We also obtain the scaling limit of the density profile of the system, which strongly resembles earlier results of Belitsky and Ferrari.