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Conditioning Bienaymé–Galton–Watson trees to have large sub-populations

Part of: Markov processes Probability theory on algebraic and topological structures

Published online by Cambridge University Press:  10 September 2025

Romain Abraham ,
Hongwei Bi  and
Jean-François Delmas
Romain Abraham*
Affiliation:
Université d’Orléans, Université de Tours, CNRS
Hongwei Bi*
Affiliation:
University of International Business and Economics
Jean-François Delmas*
Affiliation:
École des Ponts
*
*Postal address: Institut Denis Poisson, Université d’Orléans, Université de Tours, CNRS, Tours, France. Email: romain.abraham@univ-orleans.fr
*Postal address: Institut Denis Poisson, Université d’Orléans, Université de Tours, CNRS, Tours, France. Email: romain.abraham@univ-orleans.fr
*Postal address: Institut Denis Poisson, Université d’Orléans, Université de Tours, CNRS, Tours, France. Email: romain.abraham@univ-orleans.fr
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Abstract

We study the local limit in distribution of Bienaymé–Galton–Watson trees conditioned on having large sub-populations. Assuming a generic and aperiodic condition on the offspring distribution, we prove the existence of a limit given by a Kesten’s tree associated with a certain critical offspring distribution.

Keywords

Bienaymé–Galton–Watson treegeneric probability distributionlocal limit

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60B10: Convergence of probability measures

Information

Type
Original Article
Information
Advances in Applied Probability , First View , pp. 1 - 42
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Applied Probability Trust

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