Abstract
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.
Bertoin, Jean