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Self-intersections of random walks on discrete groups

Published online by Cambridge University Press:  24 October 2008

David J. Aldous
David J. Aldous
Affiliation:
Department of Statistics, University of California, Berkeley, CA 94720, U.S.A.
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Extract

For a random walk on a finite group, the distribution after n steps will converge, as n→∞, to the uniform distribution (under mild conditions). The asymptotic behaviour of such walks can be studied easily using standard Markov chain theory. But there are many natural problems about the non-asymptotic behaviour which have no simple solution in general. For example, what is

the time until a specified element is first visited?

the time until all element have been visited?

the time until the distribution approaches the uniform distribution?

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 98 , Issue 1 , July 1985 , pp. 155 - 177
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

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