A line-breaking construction of the stable trees
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| Description: |
Goldschmidt, C (University of Oxford)
Monday 16 March 2015, 15:30-16:30 |
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| Created: | 2015-03-17 17:42 |
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| Collection: | Random Geometry |
| Publisher: | Isaac Newton Institute |
| Copyright: | Goldschmidt, C |
| Language: | eng (English) |
| Distribution: |
World
(downloadable)
|
| Explicit content: | No |
| Aspect Ratio: | 16:9 |
| Screencast: | No |
| Bumper: | UCS Default |
| Trailer: | UCS Default |
| 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. |
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