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Random Multiplication Approaches Uniform Measure in Finite Groups

Author

Listed:
  • A. Abrams

    (Emory University)

  • H. Landau
  • Z. Landau

    (City College of New York)

  • J. Pommersheim

    (Reed College)

  • E. Zaslow

    (Northwestern University)

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

Suggested Citation

  • A. Abrams & H. Landau & Z. Landau & J. Pommersheim & E. Zaslow, 2007. "Random Multiplication Approaches Uniform Measure in Finite Groups," Journal of Theoretical Probability, Springer, vol. 20(1), pages 107-118, March.
    • Handle: RePEc:spr:jotpro:v:20:y:2007:i:1:d:10.1007_s10959-006-0051-0
    DOI: 10.1007/s10959-006-0051-0
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    Cited by:

    1. Yang, Li & Hu, Jiang & Bai, Zhidong, 2024. "Revisit of a Diaconis urn model," Stochastic Processes and their Applications, Elsevier, vol. 172(C).

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