Non Markovianity of the Boltzmann-Grad limit of a system of random obstacles in a given force field

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.