Branching Processes with Biological Applications

By Xiaowei Wu. 2010

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Universality for first passage percolation on sparse random graphs (2012, methodology): “We make use of second moment methods similar to the ones in [21, 24, 25, 38], but with a suitable truncation argument to circumvent the problem of infinite-variance offspring distributions.”
Fringe trees, Crump-Mode-Jagers branching processes and $m$-ary search trees (2016, background): “[71; 72; 104; 105], is a random function φ(t) of the age t > 0; we assume that φ(t) > 0 and that φ belongs to”
Branching random walks (2015, background): “If t > 0 is such that ψ(t) = 0, the value of t is often referred to as a “Malthusian parameter” in various contexts (Jagers [147], Nerman [202], Bertoin [47], etc.”
Large deviations for Markovian nonlinear Hawkes processes (2011, background): “…the good rate function I ( ), i.e. for any closed set C ⊂ R , (1.4) lim sup and for any open set G ⊂ R , where It is well known that, for instance, see page 39 of Jagers [12], for all (cid:8) (cid:9) See Dembo and Zeitouni [5] for general background regarding large deviations and the applications.”
Population Dynamics and Random Genealogies (2008, background): “On branching models and random trees, book references include Refs.[5,6,32,39,53,55,62].”