Rapid mixing of dealer shuffles and clumpy shuffles
نویسندگان
چکیده
منابع مشابه
Rapid mixing of dealer shuffles and clumpy shuffles
A famous result of Bayer and Diaconis [2] is that the Gilbert-Shannon-Reeds (GSR) model for the riffle shuffle of n cards mixes in 3 2 log2 n steps and that for 52 cards about 7 shuffles suffices to mix the deck. In this paper, we study variants of the GSR shuffle that have been proposed to model more realistically how people actually shuffle a deck of cards. The clumpy riffle shuffle and deale...
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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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Consider a deck of n cards. Let p1, p2, . . . , pn be a probability vector and consider the mixing time of the card shuffle which at each step of time picks a position according to the pi’s and move the card in that position to the top. This setup was introduced in [5], where a few special cases were studied. In particular the case pn−k = pn = 1/2, k = Θ(n), turned out to be challenging and onl...
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ژورنال
عنوان ژورنال: Electronic Communications in Probability
سال: 2015
ISSN: 1083-589X
DOI: 10.1214/ecp.v20-3682