2021/11/08 by Serik Sagitov, Sagitov, Serik
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Evolution and Genetic Dynamics #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR
paper · pdf · doi:10.48550/arxiv.2111.04274
17 pages, 1 figure
openalex publication_date 2021/11/08 · arxiv created 2022/04/05 · arxiv updated 2022/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the critical Galton-Watson process with overlapping generations stemming from a single founder. Assuming that both the variance of the offspring number and the average generation length are finite, we establish the convergence of the finite-dimensional distributions, conditioned on non-extinction at a remote time of observation. The limiting process is identified as a pure death process coming down from infinity. This result brings a new perspective on Vatutin's dichotomy claiming that in the critical regime of age-dependent reproduction, an extant population either contains a large number of short-living individuals or consists of few long-living individuals.