Gravitational clustering and additive coalescence

We investigate a gravitational system in dimension one, started from some “uniform” random initial data. In Section 2, a connection is established with the additive coalescent. An hydrodynamic limit is obtained in Section 3 and it suggests a new construction of the standard additive coalescent. The latter is given in Section 3.2. An infinite system is considered in Section 4, and is shown to be closely related to the Smoluchowski additive and multiplicative equations.