Probability Surveys

A survey of results on random random walks on finite groups

Martin Hildebrand

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A number of papers have examined various aspects of “random random walks” on finite groups; the purpose of this article is to provide a survey of this work and to show, bring together, and discuss some of the arguments and results in this work. This article also provides a number of exercises. Some exercises involve straightforward computations; others involve proving details in proofs or extending results proved in the article. This article also describes some problems for further study.

Article information

Probab. Surveys, Volume 2 (2005), 33-63.

First available in Project Euclid: 28 February 2005

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60-02: Research exposition (monographs, survey articles)
Secondary: 60B15: Probability measures on groups or semigroups, Fourier transforms, factorization

random walk finite group Upper Bound Lemma Fourier analysis


Hildebrand, Martin. A survey of results on random random walks on finite groups. Probab. Surveys 2 (2005), 33--63. doi:10.1214/154957805100000087.

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