 
Summary: DOI: 10.1007/s1095900600510
Journal of Theoretical Probability (© 2007)
Random Multiplication Approaches Uniform Measure
in Finite Groups
A. Abrams,1,6 H. Landau,2 Z. Landau,3 J. Pommersheim,4 and E. Zaslow5
Received October 24, 2004
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 .
KEY WORDS: Finite group; random process; uniform distribution.
1. INTRODUCTION
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
