Non Markovian behavior of the Boltzmann-Grad limit of linear stochastic particle systems. (English) Zbl 1138.82026

Ricci, Valeria

Commun. Math. Sci. 1, Suppl., 95-105 (2007).

Summary: We 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. We 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.

MSC:

82C40	Kinetic theory of gases in time-dependent statistical mechanics
82C21	Dynamic continuum models (systems of particles, etc.) in time-dependent statistical mechanics
60K35	Interacting random processes; statistical mechanics type models; percolation theory

Keywords:

linear Boltzmann equation; Lorentz gas; lattice gas; force field; non Markovian