Conditioning Bienaym{\'e}-Galton-Watson trees to have large sub-populations

Romain Abraham; Hongwei Bi; Jean-François Delmas

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arXiv · 2311.17716

Conditioning Bienaym{\'e}-Galton-Watson trees to have large sub-populations

Romain Abraham·Hongwei Bi·Jean-François Delmas

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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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Romain Abraham, Hongwei Bi, Jean-François Delmas. 2023-11-29. Conditioning Bienaym{\'e}-Galton-Watson trees to have large sub-populations. https://arxiv.org/abs/2311.17716

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