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.