Université Paris 6
Pierre et Marie Curie | Université Paris 7
Denis Diderot | |

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**Code(s) de Classification MSC:**

- 60J65 Brownian motion, See also {58G32}
- 60J25 Markov processes with continuous parameter

**Résumé:** We establish a connection between two different models of
clustering: the deterministic model of sticky particles which describes the
evolution of a system
of infinitesimal particles governed by the dynamic of completely inelastic
shocks (i.e.
clustering occurs upon collision with conservation of masses and momenta),
and the random model of the so-called additive coalescent in which
velocities and distances
between clusters are not taken into account. The connection is obtained
when at the initial time,
the particles are uniformly distributed on a line and their velocities are
given by a Brownian
motion.

**Mots Clés:** * Sticky particles ; Brownian velocity ; Burgers equation ; coalescent ;
fragmentation*

**Date:** 1999-06-29

**Prépublication numéro:** *PMA-514*