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 \({\frac{1}{|G|}}\) .
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Abrams, A., Landau, H., Landau, Z. et al. Random Multiplication Approaches Uniform Measure in Finite Groups. J Theor Probab 20, 107–118 (2007). https://doi.org/10.1007/s10959-006-0051-0
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DOI: https://doi.org/10.1007/s10959-006-0051-0