A line-breaking construction of the stable trees

摘要

We give a new, simple construction of the $lpha$-stable tree for $lpha in (1,2]$. 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 $lpha = 2$, we recover Aldous' line-breaking construction of the Brownian continuum random tree based on an inhomogeneous Poisson process.