Electronic Journal of Probability

The genealogy of Galton-Watson trees

Samuel G.G. Johnston

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Take a continuous-time Galton-Watson tree and pick $k$ distinct particles uniformly from those alive at a time $T$. What does their genealogical tree look like? The case $k=2$ has been studied by several authors, and the near-critical asymptotics for general $k$ appear in Harris, Johnston and Roberts (2018) [9]. Here we give the full picture.

Article information

Electron. J. Probab., Volume 24 (2019), paper no. 94, 35 pp.

Received: 5 March 2019
Accepted: 26 August 2019
First available in Project Euclid: 13 September 2019

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Zentralblatt MATH identifier

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces 60J85: Applications of branching processes [See also 92Dxx]

Galton-Watson trees branching processes spines coalescence Faà di Bruno’s formula

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Johnston, Samuel G.G. The genealogy of Galton-Watson trees. Electron. J. Probab. 24 (2019), paper no. 94, 35 pp. doi:10.1214/19-EJP355. https://projecteuclid.org/euclid.ejp/1568361635

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