Open Access
2000 Coalescents with Simultaneous Multiple Collisions
Jason Schweinsberg
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Electron. J. Probab. 5: 1-50 (2000). DOI: 10.1214/EJP.v5-68


We study a family of coalescent processes that undergo ``simultaneous multiple collisions,'' meaning that many clusters of particles can merge into a single cluster at one time, and many such mergers can occur simultaneously. This family of processes, which we obtain from simple assumptions about the rates of different types of mergers, essentially coincides with a family of processes that Mohle and Sagitov obtain as a limit of scaled ancestral processes in a population model with exchangeable family sizes. We characterize the possible merger rates in terms of a single measure, show how these coalescents can be constructed from a Poisson process, and discuss some basic properties of these processes. This work generalizes some work of Pitman, who provides similar analysis for a family of coalescent processes in which many clusters can coalesce into a single cluster, but almost surely no two such mergers occur simultaneously.


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Jason Schweinsberg. "Coalescents with Simultaneous Multiple Collisions." Electron. J. Probab. 5 1 - 50, 2000.


Accepted: 10 July 2000; Published: 2000
First available in Project Euclid: 7 March 2016

zbMATH: 0959.60065
MathSciNet: MR1781024
Digital Object Identifier: 10.1214/EJP.v5-68

Primary: 60J25
Secondary: 05A18 , 60G09 , 60G55 , 60J75

Keywords: ancestral processes , Coalescence , exchangeable random partitions , Markov processes , Poisson point processes

Vol.5 • 2000
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