Long edges in Galton-Watson trees

2023/08/30 by Sergey Bocharov, Simon C. Harris, Bocharov, Sergey +1
Mathematics · Physics and Astronomy · #FOS: Biological sciences #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Populations and Evolution (q-bio.PE) #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2308.16168

openalex publication_date 2023/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we will establish a number of results concerning the limiting behaviour of the longest edges in the genealogical tree generated by a continuous-time Galton-Watson (GW) process. Separately, we consider the large time behaviour of the longest pendant edges, the longest (strictly) interior edges, and the longest of all the edges. These results extend the special case of long pendant edges of birth-death processes established in Bocharov, Harris, Kominek, Mooers, and Steel [1] .

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