Séminaires

The talk is about an ”ω-circular” *-distribution μ_ω, defined in terms of a complex parameter ω with |ω| = 1. This is the limit law in a CLT-style theorem for a sequence of ω-commuting unitaries in a *-probability space. Its name is justified by an analogy with the *-distribution of Voiculescu’s circular element in free probability. On a combinatorial level, the *-moments of μ_ω are given by summations over pair-partitions, where the pairs of the partition are ordered and the crossings between pairs have signs. The study of such summations yields recursion formulas for *-moments and, in particular, leads to a nice description of the resulting ω-Fock space. This is a joint work with Claus Koestler (Cork) and Liam McQuay (PhD student, Waterloo).

Dans ce travail, nous étudions un modèle de régression visant à décrire le comportement des valeurs extrêmes d’une variable Y à partir de covariables X. Nous proposons une méthode de réduction de dimension spécialement conçue pour les queues de distribution, permettant de surmonter le fléau de la grande dimension et d’améliorer l’estimation de l’indice des valeurs extrêmes conditionnel.