Persi Diaconis

Persi Diaconis
Persi Diaconis, 2010
Born	(1945-01-31) January 31, 1945 New York City, New York
Nationality	American
Fields	Mathematics
Institutions	Harvard University Stanford University
Alma mater	City College of New York B.S. (1971) Harvard University M.A. (1972), Ph.D. (1974)
Doctoral advisor	Dennis Arnold Hejhal Frederick Mosteller
Doctoral students	Sourav Chatterjee Igor Pak Robin Pemantle Eric Rains Jeff Rosenthal Arif Zaman

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. He is particularly known for tackling mathematical problems involving randomness and randomization, such as coin flipping and shuffling playing cards.

Card shuffling

See also: 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.

Biography

Diaconis left home at 14 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 (City College of New York for his undergraduate work graduating in 1971 and then a Ph.D. in Mathematical Statistics from Harvard University in 1974), 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.

Recognition

• 1982 – Awarded the Rollo Davidson Prize.
• 1995 - Elected to the National Academy of Sciences
• 1997 – Gibbs Lecturer, American Mathematical Society.
• 2003 – Received an honorary D. Sci. degree from the University of Chicago.
• 2006 – Awarded the Van Wijngaarden Award.
• 2012 – Awarded the Levi L. Conant Prize.
• 2012 – Fellow of the American Mathematical Society
• 2013 – Received an Honorary Degree from the University of St Andrews.

Works

• "Theories of data analysis: from magical thinking through classical statistics", in

See also

• Freedman–Diaconis rule
• Patience sorting
• Random walk
• Mathemagician

External links

• Interview: Persi Diaconis discusses his life, magic and mathematics on the 7th Avenue Project radio show