The Annals of Applied Probability

On the rate of mixing for $p$-shuffles

Steven P. Lalley

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The p-shuffle is a natural generalization of the dovetail shuffle. It is defined as follows. First, the deck is cut into a top stack and a bottom stack so that the distribution of the size of the top stack is Binomial $(N, p)$, where $N$ is the total number of cards in the deck.Then, conditional on the outcome of the cut,the two stacks are “riffled” in such a way that all possible riffles (interleavings) of these two stacks are equally likely. The main result of the paper is an asymptotic $(N \to \infty)$ bound on the number of repetitions needed to “randomize” the deck.

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Ann. Appl. Probab., Volume 10, Number 4 (2000), 1302-1321.

First available in Project Euclid: 22 April 2002

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Zentralblatt MATH identifier

Primary: 60C05: Combinatorial probability
Secondary: 60B15: Probability measures on groups or semigroups, Fourier transforms, factorization 20B30: Symmetric groups

Riffle shuffle cutoff phenomenon


Lalley, Steven P. On the rate of mixing for $p$-shuffles. Ann. Appl. Probab. 10 (2000), no. 4, 1302--1321. doi:10.1214/aoap/1019487618.

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