Analysis and probability on finite quantum groups and dual groups

In this talk, we will first present a result from Diaconis, Shahshahani and Evans. Let M be a random matrix chosen from the unitary group $U(n)$ and distributed according to the Haar measure. Then, for $j\in \mathbb N$, ${\rm Tr}(M^j)$ are independent and distributed as some complex Gaussian random variables when $n\to \infty$. We will look at this type of result in the framework of finite quantum groups and then in the unitary dual group.

Referat odbędzie się w ramach projektu Polonium, współfinansowanego przez Narodową Agencję Wymiany Akademickiej (NAWA).