Abstract
A celebrated theorem of Aldous, Bayer and Diaconis asserts that it takes ∼3/2 log 2 n riffle shuffles to randomize a deck of n cards, asymptotically as n → ∞, and that the randomization occurs abruptly according to a 9cut–off phenomenon9. These results depend upon measuring randomness by a quantity known as the total variation distance. If randomness is measured by uncertainty or entropy in the sense of information theory, the behaviour is different. It takes only ∼log 2 n shuffles to reduce the information to a proportion arbitrarily close to zero, and ∼3/2 log 2 n to reduce it to an arbitrarily small number of bits. At 3/2> log 2 n shuffles, ca .0.0601 bits remain, independently of n .
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Schedule a callMore From: Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
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