Genealogy of catalytic branching models

Popovic L, Winter A, Greven A (2009)

Publication Type: Journal article, Original article

Publication year: 2009


Publisher: Institute of Mathematical Statistics (IMS)

Book Volume: 19

Pages Range: 1243-1272

Journal Issue: 3


DOI: 10.1214/08-AAP574


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, 2009.

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How to cite


Popovic, L., Winter, A., & Greven, A. (2009). Genealogy of catalytic branching models. Annals of Applied Probability, 19(3), 1243-1272.


Popovic, Lea, Anita Winter, and Andreas Greven. "Genealogy of catalytic branching models." Annals of Applied Probability 19.3 (2009): 1243-1272.

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