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

Consider a particle moving through a random medium. The medium consists of spherical obstacles of equal radii, randomly distributed in $\mathbb R^3$. The particle is accelerated by a constant external field. When colliding with an obstacle, the particle inelastically reflects. We study asymptotics of $X(t)$, which denotes the position of the particle at time $t$, as $t\to\infty$. The result is a limit theorem for $X(t)$. Our proof is based on functional CLT for Markov chains.