Mathematics Colloquia and Seminars

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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.