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2009 A new family of Markov branching trees: the alpha-gamma model
Bo Chen, Daniel Ford, Matthias Winkel
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Electron. J. Probab. 14: 400-430 (2009). DOI: 10.1214/EJP.v14-616


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 size-biased order, and we study their limiting behaviour.


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Bo Chen. Daniel Ford. Matthias Winkel. "A new family of Markov branching trees: the alpha-gamma model." Electron. J. Probab. 14 400 - 430, 2009.


Accepted: 9 February 2009; Published: 2009
First available in Project Euclid: 1 June 2016

zbMATH: 1190.60081
MathSciNet: MR2480547
Digital Object Identifier: 10.1214/EJP.v14-616

Primary: 60J80

Keywords: Alpha-gamma tree , Continuum random tree , dislocation measure , Markov branching model , R-tree , sampling consistency , Self-similar fragmentation , splitting rule

Vol.14 • 2009
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