View source for Persi Diaconis

{{short description|American mathematician and statistician}}
{{Infobox scientist
| name              = Persi Diaconis
| image             = S Holmes-P Diaconis (cropped).jpg
| caption           = Diaconis in 2010
| birth_date        = {{birth date and age|1945|01|31|mf=y}}
| birth_place       = New York City, US
| death_date        = 
| death_place       = 
| fields            = [[Mathematical statistics]]
| workplaces        = [[Harvard University]]<br>[[Stanford University]]
| education         = [[City College of New York]] ([[Bachelor of Science|BS]])<br>[[Harvard University]] ([[Master of Arts|MA]], [[PhD]])
| doctoral_advisor  = [[Dennis Hejhal|Dennis Arnold Hejhal]]<br>[[Frederick Mosteller]]<ref>{{MathGenealogy|id=18747}}</ref>
| doctoral_students = {{plainlist|1=
*[[Sourav Chatterjee]]
*[[Eduardo Engel]]
*[[Elizabeth Meckes]]
*[[Igor Pak]]
*[[Eric Rains]]
*[[Jeff Rosenthal]]
*[[Francis Su]]
*[[Elizabeth Wilmer]]
*[[Arif Zaman]]
}}
| known_for         = [[Freedman–Diaconis rule]]
| awards            = 
| spouse            = [[Susan P. Holmes|Susan Holmes]]
}}
'''Persi Warren Diaconis''' ({{IPAc-en|ˌ|d|aɪ|ə|ˈ|k|oʊ|n|ɪ|s}}; born January 31, 1945) is an American [[mathematician]] of [[Greece|Greek]] descent and former professional [[Magic (illusion)|magician]].<ref>{{Cite journal | last1 = Hoffman | first1 = J. | title = Q&A: The mathemagician | doi = 10.1038/478457a | journal = Nature | volume = 478 | issue = 7370 | pages = 457 | year = 2011 | bibcode = 2011Natur.478..457H | doi-access = free }}</ref><ref>{{Diaconis Graham 2011}}</ref> He is the [[Mary V. Sunseri]] Professor of [[Statistics]] and [[Mathematics]] at [[Stanford University]].<ref>{{cite web |url=http://www-stat.stanford.edu/~cgates/PERSI/ |title=Stanford University - Persi Diaconis |access-date=2011-10-27 |archive-date=2011-10-11 |archive-url=https://web.archive.org/web/20111011151729/http://www-stat.stanford.edu/%7Ecgates/PERSI/ |url-status=dead }}</ref><ref>{{cite web |url=http://www.homepages.indiana.edu/022704/text/persi.shtml |title=It's no coincidence: Stanford University mathematician and statistician Persi Diaconis will serve as a Patten Lecturer at Indiana University Bloomington |access-date=2011-10-27 |url-status=dead |archive-url=https://web.archive.org/web/20111110143732/http://www.homepages.indiana.edu/022704/text/persi.shtml |archive-date=2011-11-10 }}</ref>

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 14<ref>{{Cite web |url=http://news-service.stanford.edu/news/2004/june9/diaconis-69.html |title=Lifelong debunker takes on arbiter of neutral choices |access-date=2012-04-15 |archive-date=2009-08-27 |archive-url=https://web.archive.org/web/20090827004200/http://news-service.stanford.edu/news/2004/june9/diaconis-69.html |url-status=dead }}</ref> to travel with magician [[Dai Vernon]], and was awarded a high school diploma based on grades given to him by his teachers after dropping out of [[George Washington Educational Campus|George Washington High School]].<ref>Amason, Cassidy. [https://www.gcsu.edu/sites/files/page-assets/node-808/attachments/amason.pdf#page=2 "Deterministic And Probabilistic Approaches To Card Shuffling"], [[Georgia College & State University]], November 30, 2016. Accessed February 14, 2023. "Diaconis attended George Washington High School in NYC and found himself at home as a member of the magic club.... Regardless of not being in high school, Diaconis’ teachers decided to give him grades for exams he had not taken - and he ended up graduating high school."</ref> He returned to school at age 24 to learn math, motivated to read [[William Feller]]'s famous two-volume treatise on probability theory, ''An Introduction to Probability Theory and Its Applications''. He attended the [[City College of New York]] for his undergraduate work, graduating in 1971, and then obtained a Ph.D. in Mathematical Statistics from [[Harvard University]] in 1974, learned to read Feller, and became a mathematical probabilist.<ref name="che">Jeffrey R. Young, "The Magical Mind of Persi Diaconis" ''Chronicle of Higher Education'' October 16, 2011 [http://chronicle.com/article/The-Magical-Mind-of-Persi/129404/?sid=cr]</ref>

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 dealing|second deal]] and [[Bottom dealing|bottom deal]]".<ref>[https://www.ams.org/notices/200506/fea-gardner.pdf Interview with Martin Gardner], ''[[Notices of the AMS]]'', June/July 2005.</ref>

Diaconis is married to Stanford statistics professor [[Susan P. Holmes|Susan Holmes]].<ref>{{cite web|last1=O'Conner|first1=J. J.|last2=Robertson|first2=E. F.|title=Diaconis biography|url=http://www-history.mcs.st-andrews.ac.uk/Biographies/Diaconis.html|website=MacTutor|access-date=2 April 2018}}</ref>

==Career==
Diaconis  received a [[John D. and Catherine T. MacArthur Foundation|MacArthur Fellowship]] in 1982. In 1990, he published (with [[Dave Bayer]]) a paper entitled "Trailing the Dovetail Shuffle to Its Lair"<ref>{{Cite journal | last1 = Bayer | first1 = Dave | author1-link=Dave Bayer | last2 = Diaconis | first2 = Persi | author2-link=Persi Diaconis | doi = 10.1214/aoap/1177005705 | title = Trailing the Dovetail Shuffle to its Lair | journal = The Annals of Applied Probability | volume = 2 | issue = 2 | pages = 295–313 | year = 1992 | doi-access = free }}</ref> (a term coined by magician [[Charles Jordan (magician)|Charles Jordan]] in the early 1900s) which established rigorous results on how many times a deck of playing cards must be [[Shuffle#Riffle|riffle shuffled]] before it can be considered random according to the mathematical measure [[Total variation distance of probability measures|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. When [[Entropy (information theory)|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).<ref>{{Cite journal | last1 = Trefethen | first1 = L. N. | author-link1 = Lloyd N. Trefethen | last2 = Trefethen | first2 = L. M. | author-link2 = Lloyd M. Trefethen | doi = 10.1098/rspa.2000.0625 | title = How many shuffles to randomize a deck of cards? | journal = [[Proceedings of the Royal Society of London A]] | volume = 456 | issue = 2002 | pages = 2561–2568 | year = 2000 |bibcode = 2000RSPSA.456.2561T | s2cid = 14055379 }}</ref>

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.<ref name=science_news>{{cite magazine
 | url = http://www.sciencenews.org/view/generic/id/38434/title/Shuffling_the_cards_Math_does_the_trick
 | title = Shuffling the cards: Math does the trick
 | date = November 7, 2008
 | access-date = 14 November 2008
 | magazine = Science News
 | quote = Diaconis and his colleagues are issuing an update. When dealing many gambling games, like blackjack, about four shuffles are enough
 }}</ref><ref name=persi_at_stanford>{{Cite journal | last1 = Assaf | first1 = S. | last2 = Diaconis | first2 = P. | last3 = Soundararajan | first3 = K. | doi = 10.1214/10-AAP701 | title = A rule of thumb for riffle shuffling | journal = The Annals of Applied Probability | volume = 21 | issue = 3 | pages = 843 | year = 2011 | arxiv = 0908.3462 | s2cid = 16661322 }}</ref>

Diaconis has been hired by casino executives to search for subtle flaws in their automatic card shuffling machines.  Diaconis soon found some and the horrified executives responded, "We are not pleased with your conclusions but we believe them and that's what we hired you for."<ref>Keating, Shane. [https://www.bbc.com/future/article/20221019-how-a-magician-mathematician-revealed-a-casino-loophole How a magician-mathematician revealed a casino loophole], [[BBC]], 20 October 2022.</ref>

He served on the Mathematical Sciences jury of the [[Infosys Prize]] in 2011 and 2012.

==Recognition==
*1982 – Awarded a [[MacArthur Fellowship]] 
*1982 – Awarded the [[Davidson Prize|Rollo Davidson Prize]]
*1990 – Invited Speaker of the [[International Congress of Mathematicians]] (ICM)<ref>{{cite book|author=Diaconis, Persi|chapter=Applications of group representations to statistical problems|title=Proceedings of the ICM, Kyoto, Japan|pages=1037–1048|year=1990}}</ref>
*1995 – Elected to the [[National Academy of Sciences]]
*1997 – Gibbs Lecturer, [[American Mathematical Society]]<ref>{{cite journal|title=Patterns in eigenvalues: the 70th Josiah Willard Gibbs lecture|journal=Bull. Amer. Math. Soc. (N.S.)|year=2003|volume=40|issue=2|pages=155–178|mr=1962294|doi=10.1090/s0273-0979-03-00975-3|last1=Diaconis|first1=Persi|doi-access=free}}</ref>
*1998 – Plenary Speaker of the ICM<ref>{{cite book|author=Diaconis, Persi|chapter=From shuffling cards to walking around the building: An introduction to modern Markov chain theory|title=Doc. Math. (Bielefeld) Extra Vol. ICM Berlin, 1998, vol. I|year=1998|pages=187–204|chapter-url=https://www.elibm.org/ft/10011721000}}</ref>
*2003 – Received an Honorary D. Sci. from the [[University of Chicago]]<ref>{{cite book |author=Salsburg, David |title=The lady tasting tea: how statistics revolutionized science in the twentieth century |url=https://archive.org/details/ladytastingteaho0000sals |url-access=registration |publisher=W.H. Freeman and CO |location=New York |year=2001 |isbn=0-8050-7134-2 }}. Cf. p.224</ref>
*2005 – Elected to the [[American Philosophical Society]]<ref>{{Cite web|title=APS Member History|url=https://search.amphilsoc.org/memhist/search?creator=Persi+Diaconis&title=&subject=&subdiv=&mem=&year=&year-max=&dead=&keyword=&smode=advanced|access-date=2021-05-25|website=search.amphilsoc.org}}</ref>
*2006 – Awarded the [[Van Wijngaarden Award]]
*2012 – Awarded the [[Levi L. Conant Prize]]<ref name="Kehoe2012">{{cite journal|last1=Kehoe|first1=Elaine|title=2012 Conant Prize|journal=Notices of the American Mathematical Society|volume=59|issue=4|year=2012|pages=1|issn=0002-9920|doi=10.1090/noti824|doi-access=free}}</ref>
*2012 – Fellow of the [[American Mathematical Society]]<ref>[https://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved 2012-11-10</ref>
*2013 – Received an Honorary Degree from the [[University of St Andrews]]<ref>{{cite web |url=http://www.st-andrews.ac.uk/600/events/celebration/graduationceremony/ |title=Graduation ceremony &#124; 600th Anniversary &#124; University of St Andrews - 1413-2013 |access-date=2014-04-05 |url-status=dead |archive-url=https://web.archive.org/web/20140407093041/http://www.st-andrews.ac.uk/600/events/celebration/graduationceremony/ |archive-date=2014-04-07 }}</ref>
*2014 – Recipient of [[Cahit Arf]] Lecture by [[Middle East Technical University]]

==Works==
The books written or coauthored by Diaconis include:
* ''Group Representations In Probability And Statistics'' (Institute of Mathematical Statistics, 1988)<ref>Review of ''Group Representations In Probability And Statistics'':
*{{citation|title=none|journal=Mathematical Reviews|year=1990|first=Philippe|last=Bougerol|mr=0964069}}</ref>
* ''Magical Mathematics: The Mathematical Ideas That Animate Great Magic Tricks'' (with [[Ronald L. Graham]], Princeton University Press, 2012),<ref>Reviews of ''Magical Mathematics'':
*{{citation|title=Review|newspaper=Times Higher Education|url=https://www.timeshighereducation.com/books/magical-mathematics-the-mathematical-ideas-that-animate-great-magic-tricks/418428.article|first=C. J.|last=Howls|date=15 December 2011}}
*{{citation|title=Review|journal=MAA Reviews|date=November 2011|url=https://www.maa.org/press/maa-reviews/magical-mathematics-the-mathematical-ideas-that-animate-great-magic-tricks|first=John D.|last=Cook|access-date=2019-11-24|archive-date=2020-07-14|archive-url=https://web.archive.org/web/20200714024825/https://www.maa.org/press/maa-reviews/magical-mathematics-the-mathematical-ideas-that-animate-great-magic-tricks|url-status=dead}}
*{{citation|date=December 10, 2011|newspaper=[[The Wall Street Journal]]|title=Pick a Card, Any Card|first=Alex|last=Stone|url=https://www.wsj.com/articles/SB10001424052970204826704577074501731476934}}
*{{citation|date=December 30, 2011|journal=Science News|title=Review|url=https://www.sciencenews.org/article/magical-mathematics-mathematical-ideas-animate-great-magic-tricks-persi-diaconis-and-ron}}
*{{citation|title=none|journal=Mathematical Reviews|year=2012|first=John J.|last=Watkins|mr=2858033}}
*{{citation|last=Van Osdol|first=Donovan H.|doi=10.1090/noti875|issue=7|journal=Notices of the American Mathematical Society|mr=2984988|pages=960–961|title=none|volume=59|year=2012|doi-access=free}}
*{{citation|last=Benjamin|first=Arthur|doi=10.1137/120973238|issue=3|journal=SIAM Review|mr=2985718|pages=609–612|title=none|volume=54|year=2012}}
*{{citation|date=July 2012|title=Review|url=https://euro-math-soc.eu/review/magical-mathematics|journal=EMS Reviews|first=Marco|last=Castrillon Lopez|access-date=2019-11-24|archive-date=2019-10-23|archive-url=https://web.archive.org/web/20191023161110/https://euro-math-soc.eu/review/magical-mathematics|url-status=dead}}
*{{citation|last=Robert|first=Christian|date=April 2013|doi=10.1080/09332480.2013.794620|issue=2|journal=Chance|pages=50–51|title=none|volume=26|s2cid=60760932}}</ref> winner of the 2013 [[Euler Book Prize]]<ref>{{citation|url=http://mathcomm.org/magical-mathematics-and-topological-barcodes/|title=Magical Mathematics And Topological Barcodes|publisher=Mathematical Association of America|first=Ivars|last=Peterson|author-link=Ivars Peterson|date=December 12, 2012}}</ref>
* ''Ten Great Ideas about Chance'' (with [[Brian Skyrms]], Princeton University Press, 2018)<ref>Reviews of ''Ten Great Ideas about Chance'':
*{{citation|title=Review|journal=MAA Reviews|date=November 2017|url=https://www.maa.org/press/maa-reviews/ten-great-ideas-about-chance|first=Mark|last=Hunacek}}
*{{citation|title=none|journal=Mathematical Reviews|first=David R.|last=Bickel|mr=3702017}}
*{{citation|title=Opinion 165|first=Doron|last=Zeilberger|url=http://sites.math.rutgers.edu/~zeilberg/Opinion165.html|date=December 31, 2018}}
*{{citation|last=Hilgert|first=Joachim|date=January 2018|doi=10.1007/s00591-018-0217-8|issue=1|journal=Mathematische Semesterberichte|pages=125–127|title=none|volume=65|s2cid=125603542}}
*{{citation|date=January 2018|journal=EMS Reviews|title=Review|url=https://euro-math-soc.eu/review/ten-great-ideas-about-chance|first=Adhemar|last=Bultheel}}
*{{citation|date=February 12, 2018|journal=ZME Science|title=Review|url=https://www.zmescience.com/science/book-review-ten-ideas-chance/|first=Alexandru|last=Micu}}
*{{citation|date=April 2018|journal=Leonardo|title=Review|url=https://www.leonardo.info/review/2018/04/review-of-ten-great-ideas-about-chance|first=Phil|last=Dyke}}
*{{citation|date=April 2, 2018|title=Demystifying Chance: Understanding the Secrets of Probability|journal=SIAM News|first=James|last=Case|url=https://sinews.siam.org/Details-Page/demystifying-chance-understanding-the-secrets-of-probability}}
*{{citation|date=April 5, 2018|journal=Cosmos|title=Review|url=https://www.pressreader.com/australia/cosmos/20180405/282694752722777|first=Craig|last=Cormick}}
*{{citation|last=Crilly|first=Tony|date=June 2018|doi=10.1080/17498430.2018.1478532|issue=3|journal=BSHM Bulletin: Journal of the British Society for the History of Mathematics|pages=197–199|title=none|volume=33|s2cid=125733920}}
*{{citation|last=Toller|first=Owen|date=October 2018|doi=10.1017/mag.2018.155|issue=555|journal=The Mathematical Gazette|pages=567–568|title=none|volume=102|s2cid=166165655}}
*{{citation|last=Cox|first=Louis Anthony Tony|date=November 2018|doi=10.1111/risa.13196|issue=11|journal=Risk Analysis|pages=2497–2501|title=none|volume=38|s2cid=115519379}}
*{{citation|last=Huber|first=Mark|issue=6|journal=Notices of the American Mathematical Society|mr=3929582|pages=917–921|title=none|volume=66|year=2019}}</ref>

His other publications include:
*"Theories of data analysis: from magical thinking through classical statistics", in {{cite book|editor-last1=Hoaglin|editor-first1=D.C.|title=Exploring Data Tables, Trends, and Shapes|publisher=Wiley|isbn=0-471-09776-4|year=1985|url-access=registration|url=https://archive.org/details/exploringdatatab0000unse}}
*{{Cite journal|last1=Diaconis|first1=P.|title=Statistical problems in ESP research|doi=10.1126/science.663642|journal=Science|volume=201|issue=4351|pages=131–136|year=1978|pmid=663642|bibcode=1978Sci...201..131D }}
*{{Cite journal|last1=Diaconis|first1=P.|last2=Holmes|first2=S|last3=Montgomery|first3=R|title=Dynamical bias in the coin toss|journal= SIAM Review|volume=49|issue=2|pages=211–235|year=2007|doi=10.1137/S0036144504446436 |bibcode=2007SIAMR..49..211D }}

==See also==
*[[Freedman–Diaconis rule]]
*[[Patience sorting]]
*[[Random walk]]
*[[Mathemagician]]

==References==
{{Reflist}}

==External links==
{{Scholia}}
* [http://7thavenueproject.com/post/92353298895/persi-diaconis-magic-mathematics Interview: Persi Diaconis discusses his life, magic and mathematics on the 7th Avenue Project radio show]
* {{MathGenealogy |id=18747}}

{{John von Neumann Lecturers}}
{{Authority control}}

{{DEFAULTSORT:Diaconis, Persi}}
[[Category:1945 births]]
[[Category:Members of the United States National Academy of Sciences]]
[[Category:Living people]]
[[Category:MacArthur Fellows]]
[[Category:Mathematics popularizers]]
[[Category:American probability theorists]]
[[Category:American magicians]]
[[Category:Harvard University alumni]]
[[Category:Stanford University Department of Mathematics faculty]]
[[Category:Stanford University Department of Statistics faculty]]
[[Category:Scientists at Bell Labs]]
[[Category:Presidents of the Institute of Mathematical Statistics]]
[[Category:Fellows of the American Mathematical Society]]
[[Category:Fellows of the American Statistical Association]]
[[Category:American people of Greek descent]]
[[Category:City College of New York alumni]]
[[Category:Members of the American Philosophical Society]]
[[Category:Cornell University faculty]]
[[Category:George Washington Educational Campus alumni]]
[[Category:20th-century American statisticians]]
[[Category:21st-century American statisticians]]