Random walk questions for linear quantum groups.
Résumé
We study the discrete quantum groups Gamma whose group algebra has an inner faithful representation of type pi : C*(Gamma) -> M-K(C). Such a representation can be thought of as coming from an embedding Gamma subset of 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 G. The proof uses various algebraic and probabilistic techniques.