no. 5
Functional analysis/Probability theory
Stochastic aspects of the unitary dual group
[Aspects stochastiques du groupe dual unitaire]

Présenté par : the Editorial Board

Baraquin, Isabelle1
1 Laboratoire de mathémathiques de Besançon, Université Bourgogne Franche-Comté, UMR CNRS 6623, 16, route de Gray, 25030 Besançon cedex, France
Comptes Rendus. Mathématique, Tome 357 (2019) no. 5, pp. 450-454.

Dans cette note, nous étudions la loi asymptotique de la trace de certaines matrices par rapport à la trace de Haar libre sur le groupe dual unitaire. Ces matrices sont les puissances de la matrice unitaire qui engendre l'algèbre de Brown. Nous procédons en deux étapes. Tout d'abord, nous calculons les cumulants joints d'une famille de matrices R-cyclique. Nous caractérisons ensuite la ⁎-distributions asymptotique des traces considérées, à l'aide des cumulants libres. En particulier, nous obtenons que ces traces sont des variables asymptotiquement circulaires et ⁎-libres.

In this note, we study the asymptotic properties of the ⁎-distribution of traces of some matrices, with respect to the free Haar trace on the unitary dual group. The considered matrices are powers of the unitary matrix generating the Brown algebra. We proceed in two steps, first computing the free cumulants of any R-cyclic family, then characterizing the asymptotic ⁎-distributions of the traces of powers of the generating matrix, thanks to these free cumulants. In particular, we obtain that these traces are asymptotic ⁎-free circular variables.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2019.05.001
Baraquin, Isabelle 1

1 Laboratoire de mathémathiques de Besançon, Université Bourgogne Franche-Comté, UMR CNRS 6623, 16, route de Gray, 25030 Besançon cedex, France 
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Baraquin, Isabelle. Stochastic aspects of the unitary dual group. Comptes Rendus. Mathématique, Tome 357 (2019) no. 5, pp. 450-454. doi : 10.1016/j.crma.2019.05.001. http://www.numdam.org/articles/10.1016/j.crma.2019.05.001/

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