Genealogy of catalytic branching models

Details Genealogy of catalytic branching models Genealogy of catalytic branching models

2006-06-13

arxiv.org/abs/math/0606313v2

Annals of Applied Probability 2009, Vol. 19, No. 3, 1232-1272

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/08-AAP574 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

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 $\mathbb{R}$-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.

Affiliated with

Also associated with

No associations

Rating

Genealogy of catalytic branching models does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Genealogy of catalytic branching models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Genealogy of catalytic branching models will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-46174