Random Multiplication Approaches Uniform Measure in Finite Groups

A. Abrams (), H. Landau (), Z. Landau (), J. Pommersheim () and E. Zaslow ()
Additional contact information
A. Abrams: Emory University
Z. Landau: City College of New York
J. Pommersheim: Reed College
E. Zaslow: Northwestern University

Journal of Theoretical Probability, 2007, vol. 20, issue 1, 107-118

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 $${\frac{1}{|G|}}$$ .

Keywords: Finite group; random process; uniform distribution (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/s10959-006-0051-0

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