2012/10/31 by Charles Bordenave · 15 citations
Mathematics · Medicine · Social Sciences · #Biology #Branching process #Combinatorics #Demography #Dynamics (music) #Ecology #Evolutionary Game Theory and Cooperation #Extinction (optical mineralogy) #Extinction probability #Limit (mathematics) #Mathematical analysis #Mathematical and Theoretical Epidemiology and Ecology Models #Mathematics #Paleontology #Physics #Predation #Statistical physics #Stochastic processes and statistical mechanics #Tree (set theory) #math.PR #msc:60J80
paper · pdf · doi:10.1214/ejp.v19-2361
published in Electronic Journal of Probability 19(none) (Institute of Mathematical Statistics) · 33 pages, 4 figures
openalex publication_date 2014/01/01 · arxiv created 2014/03/05 · arxiv updated 2014/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider the spreading dynamics of two nested invasion clusters on an infinite tree. This model was defined as the chase-escape model by Kordzakhia and it admits a limit process, the birth-and-assassination process, previously introduced by Aldous and Krebs. On both models, we prove an asymptotic equivalent of the extinction probability near criticality. In the subcritical regime, we give a tail bound on the total progeny of the preys before extinction.