A new family of Markov branching trees: the alpha-gamma model

Details A new family of Markov branching trees: the alpha-gamma model A new family of Markov branching trees: the alpha-gamma model

2008-07-03

arxiv.org/abs/0807.0554v1

Mathematics

Probability

23 pages, 1 figure

Scientific paper

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 Duquesne and Le Gall's 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 sized-biased order, and we study their limiting behaviour.

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