Coalescence times for the Bienaymé-Galton-Watson process. (English) Zbl 1291.60157
Summary: We investigate the distribution of the coalescence time (most recent common ancestor) for two individuals picked at random (uniformly) in the current generation of a continuous-time Bienaymé-Galton-Watson process founded \(t\) units of time ago. We also obtain limiting distributions as \(t\to \infty\) in the subcritical case. We extend our results for two individuals to the joint distribution of coalescence times for any finite number of individuals sampled in the current generation.
MSC:
| 60J27 | Continuous-time Markov processes on discrete state spaces |
| 60J80 | Branching processes (Galton-Watson, birth-and-death, etc.) |
Keywords:
Bienaymé-Galton-Watson process; coalescence; discrete-state branching process; quasistationary distributionReferences:
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