Eigenvalues of the natural random walk on the Burnside group B(3,n)
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/1176987810
发表日期：
1995
页码：
1950-1960
关键词：
摘要：
In this paper we give sharp bounds on the eigenvalues of the natural random walk on the Burnside group B(3, n). Most of the argument uses established geometric techniques for eigenvalue bounds. However, the most interesting bound, the upper bound on the second largest eigenvalue, cannot be done by existing techniques. To give a bound we use a novel method for bounding the eigenvalues of a random walk on a group G (or equivalently its Cayley graph). This method works by choosing eigenvectors which fall into representations of an Abelian normal subgroup of G. One is then left with a large number (one for each representation) of easier problems to analyze.