A functional limit theorem for the position of a particle in the Lorentz model

We consider a particle moving through a medium under a constant external field. The medium consists of immobile spherical obstacles of equal radii randomly distributed in ℝ³. When the particle collides with an obstacle, it reflects inelastically, with restitution coefficient α , (0, 1). We study the asymptotics of X(t), the position of the particle at time t, as t → ∞. The main result is a functional limit theorem for X(t). Its proof is based on the functional CLT for Markov chains. Bibliography: 10 titles.