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

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	345-386
Number of pages	42
Journal	Advances in Applied Probability
Volume	58
Issue number	1
DOIs	https://doi.org/10.1017/apr.2025.10028
Publication status	Published - 1 Mar 2026

Keywords

Bienaymé-Galton-Watson tree
generic probability distribution
local limit

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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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Y1 - 2026/3/1

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

Abstract

Keywords

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