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.
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Goldschmidt et al. (2015) studied this question.
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