Poisson boundary of the discrete quantum group A_u(F)^
We identify the Poisson boundary of the dual of the universal compact quantum group A_u(F) with a measurable field of ITPFI factors.
math.OA↗
arXiv subjects
Nikolas Vander Vennet
Publications and source records attributed to Nikolas Vander Vennet.
Actions of monoidally equivalent compact quantum groups and applications to probabilistic boundaries
Bichon, De Rijdt and Vaes introduced the notion of monoidally equivalent compact quantum groups. In this paper we prove that there is a natural bijective correspondence between actions of monoidally equivalent quantum groups on unital C*-algebras or on von Neumann algebras. We apply this correspondence to study the behavior of Poisson and Martin boundaries under monoidal equivalence of quantum groups.
math.OA↗
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.
math.OA↗