• français
    • English
  • English 
    • français
    • English
  • Login
JavaScript is disabled for your browser. Some features of this site may not work without it.
BIRD Home

Browse

This CollectionBy Issue DateAuthorsTitlesSubjectsJournals BIRDResearch centres & CollectionsBy Issue DateAuthorsTitlesSubjectsJournals

My Account

Login

Statistics

View Usage Statistics

Scaling limits of Markov branching trees, with applications to Galton-Watson and random unordered trees

Thumbnail
Date
2012
Link to item file
http://hal.archives-ouvertes.fr/hal-00464337/fr/
Dewey
Probabilités et mathématiques appliquées
Sujet
fragmentation trees; Brownian tree; stable trees; random unordered trees; Markov branching trees; scaling limits
Journal issue
Annals of Probability
Volume
40
Number
6
Publication date
2012
Article pages
2589-2666
Publisher
Institute of Mathematical Statistics
DOI
http://dx.doi.org/10.1214/11-AOP686
URI
https://basepub.dauphine.fr/handle/123456789/3816
Collections
  • CEREMADE : Publications
Metadata
Show full item record
Author
Haas, Bénédicte
Miermont, Grégory
Type
Article accepté pour publication ou publié
Abstract (EN)
We consider a family of random trees satisfying a Markov branching property. Roughly, this property says that the subtrees above some given height are independent with a law that depends only on their total size, the latter being either the number of leaves or vertices. Such families are parameterized by sequences of distributions on partitions of the integers, that determine how the size of a tree is distributed in its different subtrees. Under some natural assumption on these distributions, stipulating that ``macroscopic'' splitting events are rare, we show that Markov branching trees admit the so-called self-similar fragmentation trees as scaling limits in the Gromov-Hausdorff-Prokhorov topology. Applications include scaling limits of consistent Markov branching model, and convergence of Galton-Watson trees towards the Brownian and stable continuum random trees. We also obtain that random uniform unordered trees have the Brownian tree as a scaling limit, hence extending a result by Marckert-Miermont and fully proving a conjecture made by Aldous.

  • Accueil Bibliothèque
  • Site de l'Université Paris-Dauphine
  • Contact
SCD Paris Dauphine - Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16

 Content on this site is licensed under a Creative Commons 2.0 France (CC BY-NC-ND 2.0) license.