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Brownian excursions and random trees

David Clancy
Thursday, October 26, 2017 - 2:30pm to 3:20pm
PDL C-401

Abstract: Consider a function f∈ Cc(ℝ→ℝ+)​ which is not identically 0. We generalize the definition of a tree in such a way that we can both topologize the space of all trees and that supp f/∼f becomes a compact tree. If instead of a deterministic f​ we consider a Brownian excursion, would there be a way to determine how the random tree supp Bex/∼Bex ``looks" like? Large random trees give us a way to answer this question. This talk will formalize some of these vague concepts and outline some of the proofs in this area. 

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