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

2023/11/29 by Romain Abraham, Abraham, Romain, Hongwei Bi +3
Computer Science · Mathematics · Physics and Astronomy · #Bayesian Methods and Mixture Models #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2311.17716

openalex publication_date 2023/11/29 · openalex created_date 2023/11/30 · openalex updated_date 2026/07/28

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.

Citations

• Nearly tight universal bounds for the binomial tail probabilities

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