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Random Multiplication Approaches Uniform Measure in Finite Groups

Aaron Abrams·Henry Landau·Zeph Landau·James Pommersheim·Eric Zaslow
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Abstract

In order to study how well a finite group might be generated by repeated random multiplications, P. Diaconis suggested the following urn model. An urn contains some balls labeled by elements which generate a group G. Two are drawn at random with replacement and a ball labeled with the group product (in the order they were picked) is added to the urn. We give a proof of his conjecture that the limiting fraction of balls labeled by each group element almost surely approaches 1/|G|.

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Aaron Abrams, Henry Landau, Zeph Landau, James Pommersheim, Eric Zaslow. 2004-10-27. Random Multiplication Approaches Uniform Measure in Finite Groups. https://arxiv.org/abs/math/0410569

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