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Comparison Techniques for Random Walk on Finite Groups

Persi Diaconis and Laurent Saloff-Coste
The Annals of Probability
Vol. 21, No. 4 (Oct., 1993), pp. 2131-2156
Stable URL: http://www.jstor.org/stable/2244713
Page Count: 26
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Comparison Techniques for Random Walk on Finite Groups
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Abstract

We develop techniques for bounding the rate of convergence of a symmetric random walk on a finite group to the uniform distribution. The techniques gives bounds on the second largest (and other) eigenvalues in terms of the eigenvalues of a comparison chain with known eigenvalues. The techniques yield sharp rates for a host of previously intractable problems on the symmetric group.

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