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|.
Original language | English (US) |
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Pages (from-to) | 107-118 |
Number of pages | 12 |
Journal | Journal of Theoretical Probability |
Volume | 20 |
Issue number | 1 |
DOIs | |
State | Published - Mar 2007 |
Keywords
- Finite group
- Random process
- Uniform distribution
ASJC Scopus subject areas
- Statistics and Probability
- General Mathematics
- Statistics, Probability and Uncertainty