Riffle shuffles and their associated dynamical systems
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)].
scientific article; zbMATH DE number 1418045