Abstract
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.
Citation
Christina Goldschmidt. Bénédicte Haas. "A line-breaking construction of the stable trees." Electron. J. Probab. 20 1 - 24, 2015. https://doi.org/10.1214/EJP.v20-3690
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