Electronic Journal of Probability
- Electron. J. Probab.
- Volume 24 (2019), paper no. 94, 35 pp.
The genealogy of Galton-Watson trees
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) . Here we give the full picture.
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
Permanent link to this document
Digital Object Identifier
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]
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