A line-breaking construction of the stable trees
Goldschmidt, Christina; Haas, Bénédicte (2015), A line-breaking construction of the stable trees, Electronic Journal of Probability, 20, p. 24 p.. 10.1214/EJP.v20-3690
TypeArticle accepté pour publication ou publié
External document linkhttps://arxiv.org/abs/1407.5691v1
Journal nameElectronic Journal of Probability
Electronic Journal of Probability and Electronic Communications in Probability
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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.
Subjects / Keywordsgeneralized Mittag-Leffler distributions; Dirichlet distributions; stable Lévy trees; line-breaking
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Winkel, Matthias; Pitman, Jim; Miermont, Grégory; Haas, Bénédicte (2008-09) Article accepté pour publication ou publié