Identification of the Poisson and Martin boundaries of orthogonal   discrete quantum groups
  The Poisson and Martin boundaries for invariant random walks on the dual of the orthogonal quantum groups A_o(F), are identified with higher dimensional Podles spheres that we describe in terms of generators and relations. This provides the first such identification for random walks on non-amenable discrete quantum groups. 
Stefaan Vaes and Nikolas Vander Vennet