We will review some results which illustrate how the distribution of obstacles and the shape of the characteristic curves influence the convergence of the probability density of linear stochastic particle systems to the one particle probability density associated with a Markovian process in the Boltzmann-Grad asymptotics.
"Non Markovian Behavior of the Boltzmann-Grad Limit of Linear Stochastic Particle Systems." Commun. Math. Sci. 5 (S1) 95 - 105, February 2007.