The cutoff phenomenon for randomized riffle shuffles
نویسندگان
چکیده
منابع مشابه
The cutoff phenomenon for randomized riffle shuffles
We study the cutoff phenomenon for generalized riffle shuffles where, at each step, the deck of cards is cut into a random number of packs of multinomial sizes which are then riffled together.
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Sticky or clumpy riffle shuffles appear quite naturally in applications; however, the problem of precisely describing the convergence rate of such modified riffle shuffles has remained open for a long time. In this paper, we develop an alternative family of clumpy shuffles, and analyze their convergence rate. We then provide empirical evidence that our alternative shuffles converge at a similar...
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The well-known Gilbert-Shannon-Reeds model for riffle shuffles assumes that the cards are initially cut ‘about in half’ and then riffled together. We analyze a natural variant where the initial cut is biased. Extending results of Fulman (1998), we show a sharp cutoff in separation and L-infinity distances. This analysis is possible due to the close connection between shuffling and quasisymmetri...
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By a well-known result of Bayer and Diaconis, the maximum entropy model of the common riffle shuffle implies that the number of riffle shuffles necessary to mix a standard deck of 52 cards is either 7 or 11 — with the former number applying when the metric used to define mixing is the total variation distance and the later when it is the separation distance. This and other related results assum...
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Given a probability distribution on a totally ordered set, we define for each n ≥ 1 a related distribution on the symmetric group Sn, called the QS-distribution. It is a generalization of the q-shuffle distribution considered by Bayer, Diaconis, and Fulman. The QS-distribution is closely related to the theory of quasisymmetric functions and symmetric functions. We obtain explicit formulas in te...
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ژورنال
عنوان ژورنال: Random Structures & Algorithms
سال: 2007
ISSN: 1042-9832
DOI: 10.1002/rsa.20195