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The \alpha-stable trees, for \alpha \in (1, 2], are a family of random \R-trees introduced by Duquesne and Le Gall in 2002, which can be viewed as a generalisation of the Brownian continuum random tree (corresponding to the case \alpha = 2). Typically, the \alpha-stable tree is constructed by taking a normalised excursion of a spectrally positive \alpha-stable L\‘evy process, then building a height process out of this which encodes the tree. In this talk we will present an alternative construction, analogous to Aldous’ line-breaking construction of the Brownian CRT, which realises the random finite-dimensional distributions of the stable tree. Based on work with Christina Goldschmidt.
