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

Romain Abraham; Hongwei Bi; Jean François Delmas

doi:10.1017/apr.2025.10028

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

Romain Abraham
, Hongwei Bi
, Jean François Delmas

conventionnée avec l'Université d'Orléans
University of International Business and Economics

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

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.

langue originale	Anglais
Pages (de - à)	345-386
Nombre de pages	42
journal	Advances in Applied Probability
Volume	58
Numéro de publication	1
Les DOIs	https://doi.org/10.1017/apr.2025.10028
état	Publié - 1 mars 2026

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10.1017/apr.2025.10028

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abstract = "We study the local limit in distribution of Bienaym{\'e}-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.",

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AU - Bi, Hongwei

AU - Delmas, Jean François

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N2 - 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.

AB - 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.

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KW - generic probability distribution

KW - local limit

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DO - 10.1017/apr.2025.10028

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

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