Interactions between Ehrenfest's urns arising from group actions

2015/09/24 by Hiroshi Mizukawa, Mizukawa, Hiroshi · 1 citation
Mathematics · Medicine · Physics and Astronomy · #Advanced Neuroimaging Techniques and Applications #FOS: Mathematics #Probability (math.PR) #Representation Theory (math.RT) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR #math.RT

paper · pdf · doi:10.48550/arxiv.1509.07248

openalex publication_date 2015/09/24 · arxiv created 2016/01/15 · arxiv updated 2016/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Ehrenfest's diffusion model is a well-known classical physical model consisting of two urns and n balls. A group theoretical interpretation of the model by using the Gelfand pair (Z/2Zwr S_n,S_n) is provided by Diaconis-Shahshahani. This interpretation remains valid for an r-urns generalization, in which case, the corresponding Gelfand pair is (S_rwr S_n,S_r-1wr S_n). In these models, there are no restrictions for ball movements, i.e., each balls can freely move to any urn. This paper introduces interactions between urns arising from actions of finite groups. The degree of freedom of ball movements is restricted by finite groups actions. Furthermore, for some cases, the existence of the cut-off phenomenons is shown.

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