Rifle Shuffles and Their Associated Dynamical Systems

Steven P. Lalley ()
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Steven P. Lalley: Purdue University

Journal of Theoretical Probability, 1999, vol. 12, issue 4, 903-932

Abstract: Abstract 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.

Keywords: Card-shuffling process; mixing; entropy; riffle-shuffles (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1023/A:1021636902356

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