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 the rst author in 7]. The model consists of point-like particles moving with velocities 1 which coalesce and chose a fresh velocity with the same distribution, when colliding. In the previous paper 7] various identities in law were derived for the innnitely extended system. In the present Note 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 nite number of individual particle trajectories in this system. We also obtain the scaling limit of the density proole of the system, which strongly resembles earlier results of Belitsky-Ferrari 2].