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Random Lazy Random Walks on Arbitrary Finite Groups

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  • Martin Hildebrand

    (State University of New York, University at Albany)

Abstract

This paper considers “lazy” random walks supported on a random subset of k elements of a finite group G with order n. If k=⌈a log2 n⌉ where a>1 is constant, then most such walks take no more than a multiple of log2 n steps to get close to uniformly distributed on G. If k=log2 n+f(n) where f(n)→∞ and f(n)/log2 n→0 as n→∞, then most such walks take no more than a multiple of (log2 n) ln(log2 n) steps to get close to uniformly distributed. To get these results, this paper extends techniques of Erdös and Rényi and of Pak.

Suggested Citation

  • Martin Hildebrand, 2001. "Random Lazy Random Walks on Arbitrary Finite Groups," Journal of Theoretical Probability, Springer, vol. 14(4), pages 1019-1034, October.
    • Handle: RePEc:spr:jotpro:v:14:y:2001:i:4:d:10.1023_a:1012529020690
    DOI: 10.1023/A:1012529020690
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    References listed on IDEAS

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    1. Nan Ting Chou & William H. Dare & William Dukes & Christopher K. Ma, 1996. "Random Walks in World Money Rates," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 23(9-10), pages 1453-1465, December.
    2. Dai, Jack J., 1998. "Some results concerning the rates of convergence of random walks on finite group," Statistics & Probability Letters, Elsevier, vol. 37(1), pages 15-17, January.
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