Electronic Journal of Probability

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

Bo Chen, Daniel Ford, and Matthias Winkel

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

Article information

Source
Electron. J. Probab. Volume 14 (2009), paper no. 15, 400-430.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464819476

Digital Object Identifier
doi:10.1214/EJP.v14-616

Mathematical Reviews number (MathSciNet)
MR2480547

Zentralblatt MATH identifier
1190.60081

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

Keywords
Alpha-gamma tree splitting rule sampling consistency self-similar fragmentation dislocation measure continuum random tree R-tree Markov branching model

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Chen, Bo; Ford, Daniel; Winkel, Matthias. A new family of Markov branching trees: the alpha-gamma model. Electron. J. Probab. 14 (2009), paper no. 15, 400--430. doi:10.1214/EJP.v14-616. https://projecteuclid.org/euclid.ejp/1464819476


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