Journal of Applied Probability
- J. Appl. Probab.
- Volume 49, Number 3 (2012), 627-638.
Coalescence in critical and subcritical Galton-Watson branching processes
In a Galton-Watson branching process that is not extinct by the nth generation and has at least two individuals, pick two individuals at random by simple random sampling without replacement. Trace their lines of descent back in time till they meet. Call that generation Xn a pairwise coalescence time. Similarly, let Yn denote the coalescence time for the whole population of the nth generation conditioned on the event that it is not extinct. In this paper the distributions of Xn and Yn, and their limit behaviors as n → ∞ are discussed for both the critical and subcritical cases.
J. Appl. Probab., Volume 49, Number 3 (2012), 627-638.
First available in Project Euclid: 6 September 2012
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60F10: Large deviations
Athreya, K. B. Coalescence in critical and subcritical Galton-Watson branching processes. J. Appl. Probab. 49 (2012), no. 3, 627--638. doi:10.1239/jap/1346955322. https://projecteuclid.org/euclid.jap/1346955322