Some aspects of additive coalescents. (English) Zbl 1007.60101

Bertoin, Jean

Li, Ta Tsien (ed.) et al., Proceedings of the international congress of mathematicians, ICM 2002, Beijing, China, August 20-28, 2002. Vol. III: Invited lectures. Beijing: Higher Education Press. 15-23 (2002).

This survey paper presents the additive coalescence and its connections with random trees, Smoluchowski’s coagulation equation and sticky particle systems. It reviews recent progress in this field due to Aldous, Aldous and Pitman, Chassaing and Louchard, and the author himself. The introduction is devoted to the finite setting, which facilitates the understanding of the non-specialist.
For the entire collection see [Zbl 0993.00023].

Reviewer: Thomas Simon (Évry)

MSC:

60K35	Interacting random processes; statistical mechanics type models; percolation theory
60G51	Processes with independent increments; Lévy processes
60G09	Exchangeability for stochastic processes

Keywords:

additive coalescent; Lévy processes; ballistic aggregation