2004/10/27 by Aaron Abrams, H. G. Landau, Abrams, Aaron +8
Mathematics · #60B15 #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Limits and Structures in Graph Theory #Probability (math.PR) #math.PR #msc:60B15
paper · pdf · doi:10.48550/arxiv.math/0410569
10 pages
arxiv created 2004/10/27 · openalex publication_date 2004/10/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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|.