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
URI: https://projecteuclid.org/euclid.aoap/1245071025
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.
APA:
Popovic, L., Winter, A., & Greven, A. (2009). Genealogy of catalytic branching models. Annals of Applied Probability, 19(3), 1243-1272. https://dx.doi.org/10.1214/08-AAP574
MLA:
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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