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A line-breaking construction of the stable trees

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Date
2015
Publisher city
Paris
Link to item file
https://arxiv.org/abs/1407.5691v1
Dewey
Probabilités et mathématiques appliquées
Sujet
generalized Mittag-Leffler distributions; Dirichlet distributions; stable Lévy trees; line-breaking
Journal issue
Electronic Journal of Probability
Volume
20
Publication date
2015
Article pages
24 p.
Publisher
Electronic Journal of Probability and Electronic Communications in Probability
DOI
http://dx.doi.org/10.1214/EJP.v20-3690
URI
https://basepub.dauphine.fr/handle/123456789/13810
Collections
  • CEREMADE : Publications
Metadata
Show full item record
Author
Goldschmidt, Christina
Haas, Bénédicte
Type
Article accepté pour publication ou publié
Abstract (EN)
We give a new, simple construction of the α-stable tree for α∈(1,2]. We obtain it as the closure of an increasing sequence of R-trees inductively built by gluing together line-segments one by one. The lengths of these line-segments are related to the the increments of an increasing R+-valued Markov chain. For α=2, we recover Aldous' line-breaking construction of the Brownian continuum random tree based on an inhomogeneous Poisson process.

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