Journal of Theoretical Probability

, Volume 12, Issue 4, pp 903–932

Rifle Shuffles and Their Associated Dynamical Systems

  • Steven P. Lalley

DOI: 10.1023/A:1021636902356

Cite this article as:
Lalley, S.P. Journal of Theoretical Probability (1999) 12: 903. doi:10.1023/A:1021636902356


It is shown that for every stationary sequence of random riffle permutations there is a natural associated dynamical system consisting of random orbits in the space of sequences from a finite alphabet. For many interesting models of card-shuffling, the associated dynamical systems have simple descriptions in terms of random or deterministic measure-preserving maps of the unit interval. It is shown that the rate of mixing for a card-shuffling process is constrained by the fiber entropy h of this map: at least (log N)/h repetitions of the shuffle are needed to randomize a deck of size N, when N is large.

Card-shuffling process mixing entropy riffle-shuffles 

Copyright information

© Plenum Publishing Corporation 1999

Authors and Affiliations

  • Steven P. Lalley
    • 1
  1. 1.Department of StatisticsPurdue UniversityWest Lafayette

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