2010/04/18 by Xiao'ou Cao, Cao, Xiao'ou, Matthias Winkel +1
Chemistry · Mathematics · Physics and Astronomy · #60J80 #Bernoulli's principle #Branching (polymer chemistry) #Branching process #Chemistry #Combinatorics #Distribution (mathematics) #FOS: Mathematics #Genealogy #Geography #History #Immigration #Markov Chains and Monte Carlo Methods #Mathematical analysis #Mathematics #Physics #Probability (math.PR) #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR #msc:60J80
paper · pdf · doi:10.48550/arxiv.1004.3061
31 pages, 2 figures
arxiv created 2010/04/18 · openalex publication_date 2010/04/18 · arxiv updated 2010/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study certain consistent families (Fλ)λ≥ 0 of Galton-Watson forests with lifetimes as edge lengths and/or immigrants as progenitors of the trees in Fλ. Specifically, consistency here refers to the property that for each μ≤λ, the forest Fμ has the same distribution as the subforest of Fλ spanned by the black leaves in a Bernoulli leaf colouring, where each leaf of Fλ is coloured in black independently with probability μ/λ. The case of exponentially distributed lifetimes and no immigration was studied by Duquesne and Winkel and related to the genealogy of Markovian continuous-state branching processes. We characterise here such families in the framework of arbitrary lifetime distributions and immigration according to a renewal process, related to Sagitov's (non-Markovian) generalisation of continuous-state branching renewal processes, and similar processes with immigration.