Tejas Iyer, WIAS Berlin: The influence of competition on geneological trees associated with explosive age-dependent branching processes (Oberseminar Mathematische Stochastik)
Wednesday, 16.11.2022 17:00 im Raum SRZ 216
An age dependent branching process models the evolution of a population of individuals in continuous time. In the framework we consider, the rate at which an individual reproduces is allowed to depend on an additional source of randomness, representing, for example, a biological `fitness'. Under these conditions, we consider the structure of the geneological tree of an explosive age dependent branching process at the time of explosion, showing that, under certain reasonable hypotheses, the geneological tree contains either a single node of infinite degree, or an infinite path. We also present some sufficient criteria for the existence of an infinite path, or a node of infinite degree. In some particular cases, labelled `super-linear preferential attachment with additive/multiplicative fitness', these criteria lead to a phase transition, where, when the influence of competition from `fitness' is high enough, the geneological tree transitions from having a node of infinite degree, to an infinite path.
Based in part on joint work with Bas Lodewijks.