Camille Male - Applications of freeness over the diagonal of large random matrices
Channel: Matrices Et Graphes Aléatoires GDR CNRS
Date: 2020-11-19

Camille Male - Applications of freeness over the diagonal of large random matrices

(the video is in French.)

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.