Random multiplication approaches uniform measure in finite groups

A. Abrams*, H. Landau, Z. Landau, J. Pommersheim, Eric Zaslow

*Corresponding author for this work

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)107-118
Number of pages12
JournalJournal of Theoretical Probability
Volume20
Issue number1
DOIs
StatePublished - Mar 1 2007

Keywords

  • Finite group
  • Random process
  • Uniform distribution

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty

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