Applications of Freeness over the diagonal of large random matrices.

Abstract: Traffic probability is an extension of free probability that comes with a general notion of traffic independence. This notion encodes a large class of relation, in particular all non commutative notions of independence. For a long time, this notion had only a combinatorial presentation, limiting its field of applicability. However, an important breakthrough was achieved two years ago when we discovered a connection with the notion of freeness over the diagonal. I will illustrate this connection with three results: - a general asymptotic freeness theorem for a very general class of random matrices - a method for computing outliers in spiked random matrix models with a variance profile - a characterization of the fluctuations of linear statistics for large Wigner matrices.

statistical mechanicsmathematical physicsprobability

Audience: researchers in the topic

Séminaire MEGA

Series comments: Description: Monthly seminar on random matrices and random graphs