Limit velocity for a driven particle in a random medium with mass aggregation

We study a one-dimensional infinite system of particles driven by a constan t positive force F which acts only on the leftmost particle which is regard ed as the tracer particle (t.p.). All other particles are field neutral, do not interact among themselves, and independently of each other with probab ility 0 < p <less than or equal to> 1 are either perfectly inelastic and "s tick" to the t.p. after the first collision, or with probability 1 - p are perfectly elastic, mechanically identical and have the same mass m. At init ial time all particles are at rest, and the initial measure is such that th e interparticle distances xi (i)'s are i.i.d. r.v.'s. with absolutely conti nuous density. We show that for any value of the field F > 0, the velocity of the t.p. converges to a limit value, which we compute, (C) 2000 Editions scientifiques et medicales Elsevier SAS.