Riffle shuffles and their associated dynamical systems
type: Item
instance of: scholarly article
title: Riffle shuffles and their associated dynamical systems
zbMATH Open document ID: 0965.60022
DOI: 10.1023/A:1021636902356
author: Steven P. Lalley
published in: Journal of Theoretical Probability
publication date: 2001-07-25T00:00:00Z
review text: With every stationary sequence of random riffle permutations the author associates a dynamical system consisting of random orbits in the space of sequences from a finite alphabet. For many models of card-shuffling (e.g.\ perfect, Borel, Fibonacci, \((u,v)\)-weighted shuffles, variants of GSR shuffle, and \(f\)-shuffle), the associated dynamical systems have simple descriptions in terms of random or deterministic measure-preserving maps of the unit interval. As a size \(N\) of a deck becomes large, the rate of mixing for a card-shuffling is prescribed by the fiber entropy. See also \textit{P.~Diaconis, M.~McGrath} and \textit{J.~Pitman} [Combinatorica 15, No. 1, 11-29 (1995; Zbl 0828.05003)].
reviewed by: Ilya Pavlyukevich
Mathematics Subject Classification ID: 60C05
Mathematics Subject Classification ID: 01A15
Mathematics Subject Classification ID: 37A05
Mathematics Subject Classification ID: 37A25
Mathematics Subject Classification ID: 37A50
zbMATH DE Number: 1418045
zbMATH Keywords: card-shuffling process
zbMATH Keywords: mixing
zbMATH Keywords: entropy
zbMATH Keywords: riffle shuffles
zbMATH Keywords: dynamical systems
zbMATH Keywords: fiber entropy
zbMATH Keywords: permutation group
MaRDI profile type: Publication
full work available at URL: a:1021636902356
OpenAlex ID: W2229795429
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description: scientific article; zbMATH DE number 1418045