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Recurrence and Transience for a Card Shuffling Model

Published online by Cambridge University Press:  12 September 2008

Gregory F. Lawler
Gregory F. Lawler
Affiliation:
Department of Mathematics, Duke University, Box 90320, Durham, NC 27708–0320, USA
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Abstract

A rule for shuffling an infinite deck of cards is considered where at each time step the first and jth card are interchanged with probability pj. Conditions are given under which this shuffling scheme, considered as a Markov chain on the space of permutations of integers, is recurrent or transient.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 4 , Issue 2 , June 1995 , pp. 133 - 142
Copyright
Copyright © Cambridge University Press 1995

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References

[1]Diaconis, P. (1988) Applications of Non-Commutative Fourier Analysis to Probability Problems. Lecture Notes in Mathematics, vol. 1362, Springer-Verlag, 51–100.Google Scholar
[2]Diaconis, P and Shahshahani, M. (1981) Generating a Random Permutation with Random Transpositions. Z. Wahr. verw. Geb. 57 159–180.CrossRefGoogle Scholar
[3]Wanding, D. and Lawler, G. To appear.Google Scholar
[4]Liggett, T. (1985) Interacting Particle Systems. Springer-Verlag.CrossRefGoogle Scholar