On Card Shuffling

  • Date: 02/28/2007

Nathanaƫl Berestycki (University of British Columbia)


University of British Columbia


I will talk about some famous results of Bayer and Diaconis (1992)
which permit a rigorous answer to the following question: given a deck
of n cards, how many times should it be shuffled so that the deck is in
approximately random order? The goal is to prove the existence of a
cutoff phenomenon: if the deck is shuffled less than (3/2)log(n) times
it is 'far' from being random but after that it is 'very close' to
being random. Aside from practical interest (in casinos and magic
tricks) and from having made the front page of the New York Times, this
leads to some really beautiful mathematical developments. The level of
the talk will be as basic as possible.

Other Information: 

Probability Seminar 2007