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:**

- 70F10 $n$-body problem
- 60G50 Sums of independent random variables

**Résumé:** We study a system of
gravitationally interacting sticky particles.
At the initial time, we have $n$ particles, each with mass $1/n$ and
momentum 0, independently spread on $[0,1]$ according to the uniform
law. Due to the confining of the system, all particles merge
into a single cluster after a finite time. We give the asymptotic laws
of the time of the last collision and of the time
of the $k$-th collision, when $n\to\infty$. We prove also
that clusters of size $k$ appear at time $\sim n^{-1/2(k-1)}$. We then
investigate the system at a fixed time $t<1$. We show that the biggest
cluster has size of order $\log n$, whereas a typical cluster is of
finite size.

**Mots Clés:** *sticky particles ; gravitational interacting ; uniform law ; Brownian bridge*

**Date:** 2001-06-13

**Prépublication numéro:** *PMA-668*