Cahiers du CEREMADE

Unité Mixte de Recherche du C.N.R.S. N°7534
Abstract : 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 beta-splitting models and Ford 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.
Continuum tree asymptotics of discrete fragmentations and applications to phylogenetic models
HAAS Bénédicte, MIERMONT Grégory, PITMAN Jim
WINKEL Matthias
Université de PARIS - DAUPHINE
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