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Article Dans Une Revue Annals of Probability Année : 2008

Continuum tree asymptotics of discrete fragmentations and applications to phylogenetic models

Résumé

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.

Dates et versions

hal-00359720 , version 1 (09-02-2009)

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Bénédicte Haas, Grégory Miermont, Jim Pitman, Matthias Winkel. Continuum tree asymptotics of discrete fragmentations and applications to phylogenetic models. Annals of Probability, 2008, 36 (5), pp.1790-1837. ⟨10.1214/07-AOP377⟩. ⟨hal-00359720⟩
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