Year: 2025
Type: article
Abstract: We establish a number of results concerning the limiting behaviour of the longest edges in the genealogical tree generated by a continuous-time Galton–Watson 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 et al. (2023).
Source: Journal of Applied Probability
DOI: 10.1017/jpr.2024.110
Authors: Sergey Bocharov, Simon C. Harris
Institutions: Xi’an Jiaotong-Liverpool University, University of Auckland
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4407714911