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Math Colloquium
Solesne Bourguin
Carnegie Melllon University
Title: Semicircular limits and transfer principles on the free Poisson chaos

Abstract: Analysis on the Poisson space has proven to have very diverse applications in fields such as such as stochastic geometry, cosmological statistics and modeling for telecommunications, among others. Motivated by understanding the intricate combinatorial structure of the Poisson chaos, which would yield new general limit theorems for Poisson functionals, we define, construct and study the free Poisson chaos, a non-commutative counterpart of the classic Poisson space. In this combinatorially different setting, we are able to prove these general limit theorems and provide a so-called "transfer principle" between the classic and non-commutative settings, allowing us to "transfer" some of the non-commutative results back to the classic case. We are also currently working on completing the remaining missing links between the two worlds by using additional tools from non-commutative probability theory.

Date: Wednesday, January 14, 2015
Time: 4:30 pm
Location: Wean Hall 8220
Submitted by:  Bohman
Note: Refreshments at 4:00 pm, Wean Hall 6220.