Genealogy of catalytic branching models - Popovic, Lea; Winter, Anita; Greven, Andreas (Annals of Applied Probability, 2009)
We consider catalytic branching populations. They consist of a catalyst population evolving according to a critical binary branching process in continuous time with a constant branching rate and a reactant population with a branching rate proportional to the number of catalyst individuals alive. The reactant forms a process in random medium. We describe asymptotically the genealogy of catalytic branching populations coded as the induced forest of R-trees using the many individuals-rapid branching continuum limit. The limiting continuum genealogical forests are then studied in detail from both the quenched and annealed points of view. The result is obtained by constructing a contour process and analyzing the appropriately rescaled version and its limit. The genealogy of the limiting forest is described by a point process. We compare geometric properties and statistics of the reactant limit forest with those of the "classical" forest. © Institute of Mathematical Statistics, 200
UnivIS-Import:2015-03-09:Pub.2009.nat.dma.lma5.geneal
Keywords: Catalytic branching; Contour process; Genealogical point processes; Gromov-hausdorff topology; R-trees; Random evolution; Random trees