Open Access
June 2009 Genealogy of catalytic branching models
Andreas Greven, Lea Popovic, Anita Winter
Ann. Appl. Probab. 19(3): 1232-1272 (June 2009). 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.


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Andreas Greven. Lea Popovic. Anita Winter. "Genealogy of catalytic branching models." Ann. Appl. Probab. 19 (3) 1232 - 1272, June 2009.


Published: June 2009
First available in Project Euclid: 15 June 2009

zbMATH: 1178.60057
MathSciNet: MR2537365
Digital Object Identifier: 10.1214/08-AAP574

Primary: 60B11 , 60J80 , 60K37 , 92D25

Keywords: Catalytic branching , contour process , genealogical point processes , Gromov–Hausdorff topology , random evolution , Random trees , R-trees

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.19 • No. 3 • June 2009
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