The Annals of Probability

Comparison Techniques for Random Walk on Finite Groups

Persi Diaconis and Laurent Saloff-Coste

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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.

Article information

Source
Ann. Probab., Volume 21, Number 4 (1993), 2131-2156.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176989013

Digital Object Identifier
doi:10.1214/aop/1176989013

Mathematical Reviews number (MathSciNet)
MR1245303

Zentralblatt MATH identifier
0790.60011

JSTOR
links.jstor.org

Subjects
Primary: 20B30: Symmetric groups
Secondary: 60B15: Probability measures on groups or semigroups, Fourier transforms, factorization 60J05: Discrete-time Markov processes on general state spaces 60F99: None of the above, but in this section

Keywords
Card shuffling reversible Markov chains random walk groups eigenvalues

Citation

Diaconis, Persi; Saloff-Coste, Laurent. Comparison Techniques for Random Walk on Finite Groups. Ann. Probab. 21 (1993), no. 4, 2131--2156. doi:10.1214/aop/1176989013. https://projecteuclid.org/euclid.aop/1176989013


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