Quantum reflections, random walks and cut-off (1802.09402v2)

Abstract: We study the cut-off phenomenon for random walks on free unitary quantum groups coming from quantum conjugacy classes of classical reflections. We obtain in particular a quantum analogue of the result of U. Porod concerning certain mixtures of such reflections. We also study random walks on quantum reflection groups and more generally free wreath products of finite group by quantum permutation groups.