The cut-off phenomenon for random reflections
成果类型：
Article
署名作者：
Porod, U
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
发表日期：
1996
页码：
74-96
关键词：
摘要：
For many random walks on ''sufficiently large'' finite groups the so-called cut-off phenomenon occurs: roughly stated, there exists a number k(0), depending on the size of the group, such that it, steps are necessary and sufficient for the random walk to closely approximate uniformity. As a first example on a continuous group, Rosenthal recently proved the occurrence of this cut-off phenomenon for a specific random walk on SO(N). Here we present and [for the case of O(N)] prove results for random walks on O(N), U(N) and Sp(N), where the one-step distribution is a suitable probability measure concentrated on reflections. In all three cases the cut-off phenomenon occurs at K-0 = 1/2 N log N.