Journal of Applied Probability

Coalescence in critical and subcritical Galton-Watson branching processes

K. B. Athreya

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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.

Article information

J. Appl. Probab., Volume 49, Number 3 (2012), 627-638.

First available in Project Euclid: 6 September 2012

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60F10: Large deviations

Branching process coalescence critical subcritical


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.

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  • Athreya, K. B. (2012). Coalescence in the recent past in rapidly growing populations. Stoch. Process. Appl. 122, 3757–3766.
  • Athreya, K. B. and Ney, P. E. (2004). Branching Processes. Dover, Mineola, NY.
  • Geiger, J. (1999). Elementary new proofs of classical limit theorems for Galton–Watson processes. J. Appl. Prob. 36, 301–309.
  • Kallenberg, O. (1986). Random Measures, 4th edn. Academic Press, London.
  • Le Gall, J.-F. (2010). Itô's excursion theory and random trees. Stoch. Process. Appl. 120, 712–749.
  • Zubkov, A. M. (1975). Limit distribution of the distance to the nearest common ancestor. Theory Prob. Appl. 20, 602–612.