Mixing properties for mechanical motion of a charged particle in a random medium

We study a one-dimensional semi-infinite system of particles driven by a co nstant positive force F which acts only on the leftmost particle of mass M, called the heavy particle (the h.p.), and all other particles are mechanic ally identical and have the same mass m ( M. Particles interact through ela stic collisions. At initial time all neutral particles are at rest, and the initial measure is such that the interparticle distances xi (i) are i.i.d. r.v. Under conditions on the distribution of xi which imply that the minim al velocity obtained by each neutral particle after the first interaction w ith the h.p. is bigger than the drift of an associated Markovian dynamics t in which each neutral particle is annihilated after the first collision) we prove that the dynamics has a strong cluster property, and as a consequenc e, we prove existence of the discrete time limit distribution for the syste m as seen from the first particle, a psi -mixing property, a drift velocity , as well af the central limit theorem for the tracer particle.