A line-breaking construction of the stable trees - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2014

A line-breaking construction of the stable trees

Résumé

We give a new, simple construction of the $\alpha$-stable tree for $\alpha \in (1,2]$. We obtain it as the closure of an increasing sequence of $\mathbb{R}$-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 $\mathbb{R}_+$-valued Markov chain. For $\alpha = 2$, we recover Aldous' line-breaking construction of the Brownian continuum random tree based on an inhomogeneous Poisson process.

Dates et versions

hal-01037930 , version 1 (23-07-2014)

Identifiants

Citer

Christina Goldschmidt, Bénédicte Haas. A line-breaking construction of the stable trees. 2014. ⟨hal-01037930⟩
98 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More