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

2008/07/03 by Bo Chen, Chen, Bo, Daniel Ford +3 · 1 citation
Mathematics · Physics and Astronomy · #60J80 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR #msc:60J80

paper · pdf · doi:10.48550/arxiv.0807.0554

23 pages, 1 figure

arxiv created 2008/07/03 · openalex publication_date 2008/07/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• The Genealogy of Self-similar Fragmentations with Negative Index as a Continuum Random Tree
• Convergence in distribution of random metric measure spaces: (Lambda-coalescent measure trees)

Cited by

• The space of multifurcating ranked tree shapes: enumeration, lattice structure, and Markov chains

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