A line-breaking construction of the stable trees
1 hour 2 mins,
114.38 MB,
MP3
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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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