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

  • Authors:

  • Miroslav Tanushev;Richard Arratia

  • Affiliations:

  • Department of Mathematics, California State University, Northridge, CA 91330–/8313, USA/ (e-mail: miroslav.tanushev@csun.edu);Department of Mathematics, University of Southern California, Los Angeles, CA 90089–/1113, USA/ (e-mail: rarratia@math.usc.edu)

  • Venue:
  • Combinatorics, Probability and Computing
  • Year:
  • 1997

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Abstract

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.