The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 19, Number 3 (2009), 1232-1272.
Genealogy of catalytic branching models
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.
Ann. Appl. Probab., Volume 19, Number 3 (2009), 1232-1272.
First available in Project Euclid: 15 June 2009
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60K37: Processes in random environments 60B11: Probability theory on linear topological spaces [See also 28C20] 92D25: Population dynamics (general)
Greven, Andreas; Popovic, Lea; Winter, Anita. Genealogy of catalytic branching models. Ann. Appl. Probab. 19 (2009), no. 3, 1232--1272. doi:10.1214/08-AAP574. https://projecteuclid.org/euclid.aoap/1245071025