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Eternal additive coalescents and certain bridges with exchangeable increments. (English) Zbl 1019.60072
The author studies the additive coalescent processes, i.e., random processes which describe the evolution of the ranked sequence of masses in a system of clusters in which each pair of clusters, say with masses \(m_i\) and \(m_j,\) merges as a single cluster with mass \(m_i+m_j\) at rate \(\kappa(m_i,m_j)=m_i+m_j,\) independently of the other pairs. Aldous and Pitman have studied the asymptotic behavior of the additive coalescent processes. The author proposes a different and simpler approach to this problem based on partitions of the unit interval induced by certain bridges with exchangeable increments. The connection between additive coalescent and interval partitions is enlightened by an interpretation in terms of an aggregating server system.

MSC:
60J25 Continuous-time Markov processes on general state spaces
60G09 Exchangeability for stochastic processes
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