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Long edges in Galton–Watson trees

Part of: Markov processes

Published online by Cambridge University Press:  18 February 2025

Sergey Bocharov Open the ORCID record for Sergey Bocharov [Opens in a new window]  and
Simon C. Harris
Sergey Bocharov*
Affiliation:
Xi’an Jiaotong-Liverpool University
Simon C. Harris*
Affiliation:
University of Auckland
*
*Postal address: Department of Foundational Mathematics, Xian Jiaotong-Liverpool University, Ren’Ai Road 111, Suzhou 215123, China. Email: [email protected]
**Postal address: Department of Statistics, University of Auckland, 38 Princes Street, Auckland, 1001, New Zealand. Email: [email protected]
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Abstract

We establish a number of results concerning the limiting behaviour of the longest edges in the genealogical tree generated by a continuous-time Galton–Watson process. Separately, we consider the large-time behaviour of the longest pendant edges, the longest (strictly) interior edges, and the longest of all the edges. These results extend the special case of long pendant edges of birth–death processes established in Bocharov et al. (2023).

Keywords

Galton–Watson processextreme lifetimes

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60J85: Applications of branching processes
Type
Original Article
Information
Journal of Applied Probability , First View , pp. 1 - 16
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Applied Probability Trust

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References

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