Persi Diaconis


Persi Warren Diaconis is an American mathematician of Greek descent and former professional magician. He is the Mary V. Sunseri Professor of Statistics and Mathematics at Stanford University.
He is particularly known for tackling mathematical problems involving randomness and randomization, such as coin flipping and shuffling playing cards.

Biography

Diaconis left home at 13 to travel with sleight-of-hand legend Dai Vernon, and dropped out of high school, promising himself that he would return one day so that he could learn all of the math necessary to read William Feller's famous two-volume treatise on probability theory, An Introduction to Probability Theory and Its Applications. He returned to school, learned to read Feller, and became a mathematical probabilist.
According to Martin Gardner, at school, Diaconis supported himself by playing poker on ships between New York and South America. Gardner recalls that Diaconis had "fantastic second deal and bottom deal".
Diaconis is married to Stanford statistics professor Susan Holmes.

Career

Diaconis received a MacArthur Fellowship in 1982. In 1990, he published a paper entitled "Trailing the Dovetail Shuffle to Its Lair" 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, after which it is reduced by a factor of 2 every shuffle. When entropy is viewed as the probabilistic distance, riffle shuffling seems to take less time to mix, and the threshold phenomenon goes away.
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 drops below.5 after 7 shuffles. Separation distance is an upper bound for variation distance.

Recognition

The books written or coauthored by Diaconis include:
His other publications include: