Random walk questions for linear quantum groups

Abstract

We study the discrete quantum groups $\Gamma$ whose group algebra has an inner faithful representation of type $\pi :C^{\ast }(\Gamma )\to M_K(\mathbb{C})$. Such a representation can be thought of as coming from an embedding $\Gamma \subset U_K$. Our main result, concerning a certain class of examples of such quantum groups, is an asymptotic convergence theorem for the random walk on $\Gamma$. The proof uses various algebraic and probabilistic techniques.

27 pages