Random walks on the groups of upper triangular matrices
成果类型：
Article
署名作者：
Stong, R
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1176987809
发表日期：
1995
页码：
1939-1949
关键词：
摘要：
This paper gives sharp bounds on the eigenvalues of a natural random walk on the group of upper triangular n x n matrices over the field of characteristic p, an odd prime, with 1's on the diagonal. In particular, this includes the finite Heisenberg groups as a special case. As a consequence we get bounds on the time required to achieve randomness for these walks. Some of the steps are done using the geometric bounds on the eigenvalues of Diaconis and Stroock. However, the crucial step is done using more subtle and idiosyncratic techniques. We bound the eigenvalues inductively over a sequence of subspaces.