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Continuum tree asymptotics of discrete fragmentations and applications to phylogenetic models

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Date
2008-09
Link to item file
http://fr.arxiv.org/abs/math/0604350
Dewey
Probabilités et mathématiques appliquées
Sujet
Markov branching model; self-similar fragmentation; continuum random tree; phylogenetic tree
Journal issue
Annals of Probability
Volume
36
Number
5
Publication date
2008
Article pages
1790-1837
Publisher
Institute of Mathematical Statistics
DOI
http://dx.doi.org/10.1214/07-AOP377
URI
https://basepub.dauphine.fr/handle/123456789/605
Collections
  • CEREMADE : Publications
Metadata
Show full item record
Author
Winkel, Matthias
Pitman, Jim
Miermont, Grégory
Haas, Bénédicte
Type
Article accepté pour publication ou publié
Abstract (EN)
Given any regularly varying dislocation measure, we identify a natural self-similar fragmentation tree as scaling limit of discrete fragmentation trees with unit edge lengths. As an application, we obtain continuum random tree limits of Aldous's beta-splitting models and Ford's alpha models for phylogenetic trees. This confirms in a strong way that the whole trees grow at the same speed as the mean height of a randomly chosen leaf.

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