In this paper we consider a particle moving in a random distribution of obstacles. Each obstacle is absorbing and a fixed force field is imposed. We show rigorously that certain (very smooth) fields prevent the process obtained by the Boltzmann-Grad limit from being Markovian. Then, we propose a slightly different setting which allows this difficulty to be removed.
Ricci, V., Desvillettes, L. (2004). Non Markovianity of the Boltzmann-Grad limit of a system of random obstacles in a given force field. BULLETIN DES SCIENCES MATHEMATIQUES, 128, 39-46.
Non Markovianity of the Boltzmann-Grad limit of a system of random obstacles in a given force field
RICCI, Valeria;
2004-01-01
Abstract
In this paper we consider a particle moving in a random distribution of obstacles. Each obstacle is absorbing and a fixed force field is imposed. We show rigorously that certain (very smooth) fields prevent the process obtained by the Boltzmann-Grad limit from being Markovian. Then, we propose a slightly different setting which allows this difficulty to be removed.
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