The cut-off phenomenon for random reflections. II: Complex and quaternionic cases
We generalize the random reflections problem on \(O(N)\) considered in part I [Ann. Probab. 24, No. 1, 74-96 (1996; Zbl 0854.60068)] to the complex and quaternionic cases. We give precise estimates on the speed of convergence to stationarity for specific examples of random walks on \(U(N)\) and \(Sp(N)\) for which the one-step distribution is a certain probability measure concentrated on reflections. Our results show that in both cases the so-called cut-off phenomenon occurs at \(k_0={1\over 2} N\log N\).
scientific article; zbMATH DE number 849093