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October, 1995 Eigenvalues of the Natural Random Walk on the Burnside Group $B(3, n)$
Richard Stong
Ann. Probab. 23(4): 1950-1960 (October, 1995). DOI: 10.1214/aop/1176987810


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.


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Richard Stong. "Eigenvalues of the Natural Random Walk on the Burnside Group $B(3, n)$." Ann. Probab. 23 (4) 1950 - 1960, October, 1995.


Published: October, 1995
First available in Project Euclid: 19 April 2007

zbMATH: 0852.60077
MathSciNet: MR1379175
Digital Object Identifier: 10.1214/aop/1176987810

Primary: 60J10

Keywords: Burnside group , Eigenvalues , Random walks

Rights: Copyright © 1995 Institute of Mathematical Statistics

Vol.23 • No. 4 • October, 1995
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