F. Rezakhanlou et Je. Tarver, BOLTZMANN-GRAD LIMIT FOR A PARTICLE SYSTEM IN CONTINUUM, Annales de l'I.H.P. Probabilites et statistiques, 33(6), 1997, pp. 753-796
We examine a system of one-dimensional particles in which the particle
s travel deterministically in between stochastic collisions. The colli
sion rates are chosen so that finitely many collisions occur in a unit
interval of time, We prove the kinetic limit and subsequently derive
the discrete Boltzmann equation.