Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics

Free Probability & Random Matrices Seminar


Tuesday, April 10th, 2018

Time: 3:30-5:00 p.m.  Place: Jeffery Hall 319

Speaker: Camille Male (Bordeaux)

Title: An introduction to traffic independence

Abstract: 

The properties of the limiting non-commutative distribution of random matrices can be usually understood thanks to the symmetry of the model, e.g. Voiculescu's asymptotic free independence occurs for random matrices invariant in law by conjugation by unitary matrices. The study of random matrices invariant in law by conjugation by permutation matrices requires an extension of free probability, which motivated the speaker to introduce in 2011 the theory of traffics. A traffic is a non-commutative random variable in a space with more structure than a general non-commutative probability space, so that the notion of traffic distribution is richer than the notion of non-commutative distribution. It comes with a notion of independence which is able to encode the different notions of non-commutative independence.

The purpose of this task is to present the motivation of this theory and to play with the notion of traffic independence.

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