The out-off phenomenon for random reflections II: Complex and quaternionic cases

Summary In this paper we generalize the random reflections problem onO(N) considered in an earlier paper to the complex and quaternionic cases. We give precise estimates on the speed of convergence to stationarity for specific examples of random walks onU(N) andSp(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 atk ₀=1/2N logN.This paper is based on parts of the author's doctoral dissertation written at The Johns Hopkins University