BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:How Many Shuffles to Randomize a Deck of Cards? - Richard Brierley
  (TCM)
DTSTART:20090116T160000Z
DTEND:20090116T163000Z
UID:TALK16254@talks.cam.ac.uk
CONTACT:Daniel Cole
DESCRIPTION:"Proc. Roy. Soc. 456\, 2561 (2000) L. N. Trefethen and L. M. T
 refethen":http://journals.royalsociety.org/content/hj18bd3a1kntx189/\n\nA 
 celebrated theorem of Aldous\, Bayer and Diaconis asserts that it takes ~3
 /2 log2 n riffle shuffles to randomize a deck of n cards\, asymptotically 
 as n M X\, and that the randomization occurs abruptly according to a 'cut-
 off phenomenon'. These results depend upon measuring randomness by a quant
 ity known as the total variation distance. If randomness is measured by un
 certainty or entropy in the sense of information theory\, the behaviour is
  different. It takes only ~ log2 n shuffles to reduce the information to a
  proportion arbitrarily close to zero\, and ~ 3/2 log2 n to reduce it to a
 n arbitrarily small number of bits. At 3/2> log2 n shuffles\, ca.0.0601 bi
 ts remain\, independently of n.
LOCATION:TCM Seminar Room\, Cavendish Laboratory
END:VEVENT
END:VCALENDAR