GENEALOGY OF CATALYTIC BRANCHING MODELS

• 成果类型: Article
• 署名作者: Greven, Andreas; Popovic, Lea; Winter, Anita
• 署名单位: University of Erlangen Nuremberg; Concordia University - Canada
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/08-AAP574
• 发表日期: 2009
• 页码: 1232-1272
• 关键词: trees

摘要

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 resealed 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.