Rifle Shuffles and Their Associated Dynamical Systems
- Steven P. Lalley
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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.
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- Rifle Shuffles and Their Associated Dynamical Systems
Journal of Theoretical Probability
Volume 12, Issue 4 , pp 903-932
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers-Plenum Publishers
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- Card-shuffling process
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- Steven P. Lalley (1)
- Author Affiliations
- 1. Department of Statistics, Purdue University, Mathematical Sciences Bldg., West Lafayette, Indiana, 47907