A new family of Markov branching trees: the alpha-gamma model
By Bo Chen, Daniel J. Ford, Matthias Winkel. 2008
49 citations recorded by the source corpus.
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.
Subfields: Condensed Matter Physics, Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/adde1a78c095e988cf38c85084482b0d3ccf7459
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In Condensed Matter Physics
- Bénédicte Haas
- Grégory Miermont
- Jean-François Le Gall
- Douglas Rizzolo
- Matthias Winkel
- Jim Pitman
- Thomas Duquesne
- Jean Bertoin
In Mathematical Physics
- Bénédicte Haas
- Grégory Miermont
- Jean-François Le Gall
- Jérémie Bettinelli
- Matthias Winkel
- Douglas Rizzolo
- Jim Pitman
- C. Abraham
In Statistics and Probability
Citations in the corpus
- Scaling limits of Markov branching trees with applications to Galton–Watson and random unordered trees (2010, background): “This general statement allows to recover and improve many results of [25, 26, 32, 14] dealing specifically with Markov branching trees.”