Events
Stochastics Seminar |
| Time: Feb 25, 2016 (02:00 PM) |
| Location: Parker Hall 322 |
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Details: Speaker: Olav Kallenberg Title: Palm trees via extended Brownian snake Abstract: A Dawson-Watanabe superprocess arises in the diffusion limit from a randomly branching and evolving population in a Euclidean space. Though the limiting process $\xi$ can be thought of as a randomly evolving diffuse cloud, its genealogy is given by a discrete Yule "stick-breaking" process. A fundamental role in the theory is played by the associated Palm trees, which describe the conditional structure of ξ, given that ξt hits some specified points x1,…,xn. Though the distributions of the latter are suggested by some circumstantial evidence, a formal proof has long been elusive. In this talk, I shall indicate how my Palm tree conjecture, and much more, can be proved by an argument involving an extension of Le Gall's Brownian snake. As always, I will maintain a bird's-eye point of view, trying to avoid the subtle technicalities of the subject. |