Exact probabilities and asymptotics for the one-dimensional coalescing ideal gas (Q1965880)

A modification of the system of coalescing random walks in one dimension is considered. The present model, called as coalescing ideal gas, is an interacting particle system with particles moving with a unit speed in a fixed random direction. In the case of a collision, the two particles coalesce and the new particle chooses its direction again in random. The model is considered for both the discrete and continuous time and the basic characteristics at time \(t\), namely the probability of a first collision of a particular particle, the probability of a collision at given site, and the probability of occupancy of a given site are explicitly expressed and their asymptotic behaviour is described. It is emphasized that the crucial characteristics correspond to those of the system of coalescing random walks and can be derived with the aid of properties of a simple random walk.