A tagged particle process in the Boltzmann-Grad limit for the Broadwell modell

Summary We study a tagged particle process for a model dynamical system in which identical particles move deterministically with discrete velocities, initially starting from a random configuration. We pass to the Boltzmann-Grad limit so that the tagged particle process converges to a nontrivial process (for short times). We can show that recollisions are vanishing in this limit, and this fact may have one expect that the limiting process would be Markovian. Nevertheless it is not Markovian, for which claim we give intuitive reasoning as well as a mathematical proof.Supported in part by Grant-in-Aid for Scientific Research (No. 62302006), Ministry of Education, Science and Culture