Bas Jordans: Convergence to the boundary for random walks on discrete quantum groups

For classical random walks there exist two boundaries: the Poisson boundary and the Martin boundary. The relation between these two boundaries is described by the so-called "convergence to the boundary". For noncommutative random walks on discrete quantum groups both the Poisson boundary and Martin boundary are defined and a noncommutative analogue of convergence to the boundary can be formulated. However, no proof is known for a such a theorem. In this talk we will compare the classical and quantum version of convergence to the boundary and study this problem for \(SU_q(2)\). Moreover we will shortly discuss the behaviour with respect to monoidal equivalence.