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

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
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