# A line-breaking construction of the stable trees

Date:
Monday 16th March 2015 - 15:30 to 16:30
Venue:
INI Seminar Room 1
Abstract:
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 \alpha \in (1,2], conditioned to have total progeny n. The stable tree with parameter \alpha \in (1,2] is the scaling limit of such a tree, where the \alpha=2 case is Aldous' Brownian continuum random tree. In this talk, I will discuss a new, simple construction of the \alpha-stable tree for \alpha \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 \alpha = 2, we recover Aldous' line-breaking construction of the Brownian continuum random tree based on an inhomogeneous Poisson process.

The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.