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

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Eternal solutions to Smoluchowski's coagulation equation with additive kernel and their probabilistic interpretations


Code(s) de Classification MSC:

Résumé: The cornerstone of this work, which is partly motivated by the characterization of the so-called eternal additive coalescents by Aldous and Pitman, is an explicit expression for the general eternal solution to Smoluchowski's coagulation equation with additive kernel. This expression points at certain L\'evy processes with no negative jumps, and more precisely at a stochastic model for aggregation based on such processes, which has been recently considered by Bertoin and Miermont and is known to bear close relations with the additive coalescence. As an application, we show that the eternal solutions can be obtained from some hydrodynamic limit of the stochastic model. We also present a simple condition that ensures the existence of a smooth density for an eternal solution.

Mots Clés: Smoluchowski's coagulation equation ; additive coalescence ; Lévy process with no positive jumps.

Date: 2001-07-09

Prépublication numéro: PMA-680