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On the genealogy and coalescence times of Bienaymé-Galton-Watson branching processes

Le : 15/01/2018 11h00
Par : Thierry Huillet (Cergy-Pontoise)
Lieu : i103
Lien web :
Résumé : Coalescence processes have received a lot of attention in the context of conditional branching processes with fixed population size and non-overlapping generations. Here focus will be on similar problems in the context of the standard unconditional Bienaymé-Galton-Watson branching processes, either (sub)-critical or supercritical. Using an analytical tool, one can derive the structure of some counting aspects of the ancestral genealogy of such processes, including: the transition matrix of the ancestral count process and an integral representation of various coalescence times distributions, such as the time to most recent common ancestor of a random sample of arbitrary size, including full size. Results are illustrated on two important examples of branching mechanisms displaying either finite or infinite reproduction mean, their main interest being to offer a closed form expression for their probability generating functions at all times. Large time behaviors are investigated. Travail joint avec Nicolas Grosjean.