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First Hitting Times for Some Random Walks on Finite Groups

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  • David Gluck

    (Wayne State University)

Abstract

We consider a random walk on a finite group G based on a generating set that is a union of conjugacy classes. Let the nonnegative integer valued random variable T denote the first time the walk arrives at the identity element of G, if the starting point of the walk is uniformly distributed on G. Under suitable hypotheses, we show that the distribution function F of T is almost exponential, and we give an error term.

Suggested Citation

  • David Gluck, 1999. "First Hitting Times for Some Random Walks on Finite Groups," Journal of Theoretical Probability, Springer, vol. 12(3), pages 739-755, July.
    • Handle: RePEc:spr:jotpro:v:12:y:1999:i:3:d:10.1023_a:1021679932572
    DOI: 10.1023/A:1021679932572
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    References listed on IDEAS

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    1. Aldous, David J., 1982. "Markov chains with almost exponential hitting times," Stochastic Processes and their Applications, Elsevier, vol. 13(3), pages 305-310, September.
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    Keywords

    Random walk; finite group;

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