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Persi Diaconis
Persi Warren Diaconis (born January 31, 1945) is an American mathematician and former professional magician. He is the Mary V. Sunseri Professor of Statistics and Mathematics at Stanford University.〔(【引用サイトリンク】title=It’s no coincidence: Stanford University mathematician and statistician Persi Diaconis will serve as a Patten Lecturer at Indiana University Bloomington )〕
He is particularly known for tackling mathematical problems involving randomness and randomization, such as coin flipping and shuffling playing cards.
==Card shuffling==
Professor Diaconis received a MacArthur Fellowship in 1982. In 1992 he published (with Dave Bayer) a paper entitled ''"Trailing the Dovetail Shuffle to Its Lair"'' (a term coined by magician Charles Jordan in the early 1900s) which established rigorous results on how many times a deck of playing cards must be riffle shuffled before it can be considered random according to the mathematical measure total variation distance. Diaconis is often cited for the simplified proposition that it takes seven shuffles to randomize a deck. More precisely, Diaconis showed that, in the Gilbert–Shannon–Reeds model of how likely it is that a riffle results in a particular riffle shuffle permutation, it takes 5 riffles before the total variation distance of a 52-card deck begins to drop significantly from the maximum value of 1.0, and 7 riffles before it drops below 0.5 very quickly (a threshold phenomenon), after which it is reduced by a factor of 2 every shuffle. Interestingly, when entropy is viewed as the probabilistic distance, riffle shuffling seems to take less time to mix, and the threshold phenomenon goes away (because the entropy function is subadditive.).
Diaconis has coauthored several more recent papers expanding on his 1992 results and relating the problem of shuffling cards to other problems in mathematics. Among other things, they showed that the separation distance of an ordered blackjack deck (that is, aces on top, followed by 2's, followed by 3's, etc.) drops below .5 after 7 shuffles. Separation distance is an upper bound for variation distance.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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