Mathematics Colloquia and Seminars
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Talkin' 'bout my generationAlgebra & Discrete Mathematics
|Speaker: ||Aaron Abrams, Emory University|
|Location: ||693 Kerr|
|Start time: ||Fri, Dec 3 2004, 12:10PM|
Suppose you have an urn containing n balls, some labeled
0 and some labeled 1. You draw twice, with replacement,
and add a new ball labeled by the mod 2 sum of your draws.
Now the urn has n+1 balls. Repeat. What happens to the
fraction of 0's and 1's in the limit?
Persi Diaconis suggested the above process as a way to
generate an arbitrary finite group G by repeated random
multiplications. (In the above example G=Z/2Z.) He made
a conjecture about the limiting behavior in general; in this
talk we prove his conjecture.