The Annals of Probability

Cycle structure of riffle shuffles

Steven P. Lalley

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A class of models for riffle shuffles ("$f$-shuffles") related to certain expansive mappings of the unit interval is studied. The main result concerns the cycle structure of the resulting random permutations in $\mathscr{S}_n$ when n is large. It describes the asymptotic distribution of the number of cycles of a given length, relating this distribution to dynamical properties of the associated mapping. This result generalizes a recent result of Diaconis, McGrath and Pitman.

Article information

Ann. Probab., Volume 24, Number 1 (1996), 49-73.

First available in Project Euclid: 15 January 2003

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 05A15: Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx] 60C05

Riffle shuffle random permutation interval mapping


Lalley, Steven P. Cycle structure of riffle shuffles. Ann. Probab. 24 (1996), no. 1, 49--73. doi:10.1214/aop/1042644707.

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