A line-breaking construction of the stable trees

@inproceedings{Goldschmidt2015ALC,
  title={A line-breaking construction of the stable trees},
  author={Christina Goldschmidt and B{\'e}n{\'e}dicte Haas},
  year={2015}
}
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.