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A line-breaking construction of the stable trees

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If you have a question about this talk, please contact Mustapha Amrani.

Random Geometry

Co-author: Benedicte Haas (Universite Paris-Dauphine)

Consider a critical Galton-Watson tree whose offspring distribution lies in the domain of attraction of a stable law of parameter lpha in (1,2], conditioned to have total progeny n. The stable tree with parameter lpha in (1,2] is the scaling limit of such a tree, where the lpha=2 case is Aldous’ Brownian continuum random tree. In this talk, I will discuss a new, simple construction of the lpha-stable tree for lpha in (1,2]. We obtain it as the completion of an increasing sequence of mathbb{R}-trees built by gluing together line-segments one by one. The lengths of these line-segments are related to the increments of an increasing mathbb{R}_+-valued Markov chain. For lpha = 2, we recover Aldous’ line-breaking construction of the Brownian continuum random tree based on an inhomogeneous Poisson process.

This talk is part of the Isaac Newton Institute Seminar Series series.

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