Limiting Velocity for a Driven Tracer Particle in a Random Medium with Mass Aggregation

We study a one-dimensional innnite system of particles driven by a constant positive force F which acts only on the leftmost particle and which is regarded as the tracer particle. All other particles are eld neutral, do not interact among themselves, and independently of each other with probability 0 < p 1 are either perfectly inelastic and "stick" to the t.p. after the rst collision, or with probability 1?p are perfectly elastic, mechanically identical and have the same mass m. At initial time all particles are at rest, and initial measure is such that interparticle distances i 's are i.i.d. r.v.'s. with absolutely continuous density. We show that for any value of the eld F > 0, the velocity of the t.p. converges to a limiting value, which is determined by an associated markovian evolution.