## On Card Shuffling

- Date: 02/28/2007

NathanaĆ«l 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.

Probability Seminar 2007