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Zbl 0971.60100
Fontes, Luiz Renato G.; Jordão Neves, Eduardo; Sidoravicius, Vladas
Limit velocity for a driven particle in a random medium with mass aggregation. (English)
[J] Ann. Inst. Henri Poincaré, Probab. Stat. 36, No.6, 787-805 (2000). ISSN 0246-0203

Summary: We study a one-dimensional infinite system of particles driven by a constant positive force $F$ which acts only on the leftmost particle which is regarded as the tracer particle (t.p.). All other particles are field neutral, do not interact among themselves, and independently of each other with probability $0<p\le 1$ are either perfectly inelastic and ``stick'' 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 initial time all particles are at rest, and the initial measure is such that the interparticle distances $\xi_i$'s are i.i.d. r.v.'s. with absolutely continuous 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.

MSC 2000:: *60K35 Interacting random processes
60J27 Markov chains with continuous parameter

Keywords: mass aggregation; Markovian approximation; asymptotic velocity; infinite system of particles

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