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A Note on Distributional Equality in the Cyclic Tour Property for Markov Chains

Published online by Cambridge University Press:  01 December 1997

MIROSLAV TANUSHEV  and
RICHARD ARRATIA
MIROSLAV TANUSHEV
Affiliation:
Department of Mathematics, California State University, Northridge, CA 91330–8313, USA; (e-mail: miroslav.tanushev@csun.edu)
RICHARD ARRATIA
Affiliation:
Department of Mathematics, University of Southern California, Los Angeles, CA 90089–1113, USA; (e-mail: rarratia@math.usc.edu)
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Abstract

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The cyclic tour property has previously been an equality for the expected time to complete a tour, compared with that for the reverse tour, for reversible Markov chains. We give a simple bijection to show that the equality can be extended to the distributions involved. The bijection is based on rotation of circular words.

Information

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 6 , Issue 4 , December 1997 , pp. 493 - 496
Copyright
1997 Cambridge University Press