Random Lazy Random Walks on Arbitrary Finite Groups

Martin Hildebrand ()
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Martin Hildebrand: State University of New York, University at Albany

Journal of Theoretical Probability, 2001, vol. 14, issue 4, 1019-1034

Abstract: 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.

Keywords: random walks; finite groups; uniform distribution (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1023/A:1012529020690

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