In this paper we generalize the random reflections problem on O(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 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 k0 = 1/2N log N.
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty