## Electronic Journal of Probability

### Coalescents with Simultaneous Multiple Collisions

Jason Schweinsberg

#### Abstract

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.

#### Article information

Source
Electron. J. Probab., Volume 5 (2000), paper no. 12, 50 pp.

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

https://projecteuclid.org/euclid.ejp/1457376447

Digital Object Identifier
doi:10.1214/EJP.v5-68

Mathematical Reviews number (MathSciNet)
MR1781024

Zentralblatt MATH identifier
0959.60065

Rights

#### Citation

Schweinsberg, Jason. Coalescents with Simultaneous Multiple Collisions. Electron. J. Probab. 5 (2000), paper no. 12, 50 pp. doi:10.1214/EJP.v5-68. https://projecteuclid.org/euclid.ejp/1457376447

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