Random forests and the additive coalescent

Abstract

This chapter reviews how various representations of additive coalescent processes, whose state space may be either finite or infinite partitions, can be constructed from random trees and forests. These constructions establish deep connections between the asymptotic behaviour of additive coalescent processes and the theory of Brownian trees and excursions. There are some close parallels with the theory of multiplicative coalescents and the asymptotics of critical random graphs, described in Section 6.4.