Cycle structure of riffle shuffles
Steven P. Lalley
Source: Ann. Probab. Volume 24, Number 1
(1996), 49-73.
Abstract
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.
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Permanent link to this document: http://projecteuclid.org/euclid.aop/1042644707
Mathematical Reviews number (MathSciNet): MR1387626
Digital Object Identifier: doi:10.1214/aop/1042644707
Zentralblatt MATH identifier: 0854.05007
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Digital Object Identifier: doi:10.1214/aoap/1177005705
Project Euclid: euclid.aoap/1177005705
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