Propagation of chaos for particle systems associated with discrete Boltzmann equation

We study a class of one-dimentional lattice gas models associated with discrete Boltzmann equations. In these models particles travel as independent random walks and collide stochastically. In Rezakhanlou (1996) we derived a Boltzmann type equation for the macroscopic particle density. In this article we determine the asymptotic law of each particle in the model.