Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aldous, D. (1994). Unpublished manuscript.
Bacher, R. (1992). Valeur propre minimale du laplacien de coxeter pour le groupe symetrique. Preprint.
Diaconis, P., and Saloff-Coste, L. (1993). Comparison techniques for random walk on finite groups.Ann. Prob. 21, 2131–2156.
Diaconis, P., and Shahshahani, M. (1981). Generating a random permutation with random transpositions.Z. Wahrsch. Verw. Geb. 57, 159–179.
Flatto, L., Odlyzko, A. M., and Wales, D. B. (1985). Random shuffles and group representations.Ann. Prob. 13, 154–178.
Liggett, T. (1989). ExponentialL 2 convergence of attractive reversible nearest particle systems.Ann. Prob. 17, 403–432.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Handjani, S., Jungreis, D. Rate of convergence for shuffling cards by transpositions. J Theor Probab 9, 983–993 (1996). https://doi.org/10.1007/BF02214260
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02214260