Electronic Journal of Probability
- Electron. J. Probab.
- Volume 14 (2009), paper no. 15, 400-430.
A new family of Markov branching trees: the alpha-gamma model
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.
Electron. J. Probab. Volume 14 (2009), paper no. 15, 400-430.
Accepted: 9 February 2009
First available in Project Euclid: 1 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
This work is licensed under a Creative Commons Attribution 3.0 License.
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