Journal of Theoretical Probability

, Volume 9, Issue 4, pp 983–993 | Cite as

Rate of convergence for shuffling cards by transpositions

  • Shirin Handjani
  • Douglas Jungreis


Suppose we are given a graph with a label on each vertex and a rate assigned to each edge, and suppose that edges flip (that is, the labels at the two endpoints switch) randomly with the given rates. We consider two Markov processes on this graph: one whose states are the permutations of then labels, and one whose states are the positions of a single label. We show that for several classes of graphs these two processes have the same spectral gap.

Key Words

Spectral gap shuffling cards graphs interchange process random walk 


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  1. 1.
    Aldous, D. (1994). Unpublished manuscript.Google Scholar
  2. 2.
    Bacher, R. (1992). Valeur propre minimale du laplacien de coxeter pour le groupe symetrique. Preprint.Google Scholar
  3. 3.
    Diaconis, P., and Saloff-Coste, L. (1993). Comparison techniques for random walk on finite groups.Ann. Prob. 21, 2131–2156.Google Scholar
  4. 4.
    Diaconis, P., and Shahshahani, M. (1981). Generating a random permutation with random transpositions.Z. Wahrsch. Verw. Geb. 57, 159–179.Google Scholar
  5. 5.
    Flatto, L., Odlyzko, A. M., and Wales, D. B. (1985). Random shuffles and group representations.Ann. Prob. 13, 154–178.Google Scholar
  6. 6.
    Liggett, T. (1989). ExponentialL 2 convergence of attractive reversible nearest particle systems.Ann. Prob. 17, 403–432.Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • Shirin Handjani
    • 1
  • Douglas Jungreis
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaLos Angeles

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