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A new family of Markov branching trees: the alpha-gamma model. (English) Zbl 1190.60081
Summary: We introduce a simple tree growth process that gives rise to a new two-parameter family of discrete fragmentation trees that extends Ford’s alpha model to multifurcating trees and includes the trees obtained by uniform sampling from T. Duquesne and J.-F. Le Gall’s [“Random trees, Lévy processes and spatial branching processes”, Paris: Société Mathématique de France (2002; Zbl 1037.60074)] stable continuum random tree. We call these new trees the alpha-gamma trees. In this paper, we obtain their splitting rules, dislocation measures both in ranked order and in size-biased order, and we study their limiting behaviour.

MSC:
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
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