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November 2000 On the rate of mixing for $p$-shuffles
Steven P. Lalley
Ann. Appl. Probab. 10(4): 1302-1321 (November 2000). DOI: 10.1214/aoap/1019487618


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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Steven P. Lalley. "On the rate of mixing for $p$-shuffles." Ann. Appl. Probab. 10 (4) 1302 - 1321, November 2000.


Published: November 2000
First available in Project Euclid: 22 April 2002

zbMATH: 1073.60535
MathSciNet: MR1810876
Digital Object Identifier: 10.1214/aoap/1019487618

Primary: 60C05
Secondary: 20B30 , 60B15

Keywords: Cutoff phenomenon , Riffle shuffle

Rights: Copyright © 2000 Institute of Mathematical Statistics


Vol.10 • No. 4 • November 2000
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