Journal of Applied Probability

Coalescence in critical and subcritical Galton-Watson branching processes

K. B. Athreya

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Abstract

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

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

Dates
First available in Project Euclid: 6 September 2012

Permanent link to this document
https://projecteuclid.org/euclid.jap/1346955322

Digital Object Identifier
doi:10.1239/jap/1346955322

Mathematical Reviews number (MathSciNet)
MR3012088

Zentralblatt MATH identifier
06099424

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

Keywords
Branching process coalescence critical subcritical

Citation

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


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References

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