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Independent Linear Statistics on Finite Abelian Groups

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Abstract

We give a complete description of the class of all finite Abelian groups X for which the independence of linear statistics L 1 = α1(ξ1) + α2(ξ2) + α3(ξ3) and L 2 = β1(ξ1) + β2(ξ2) + β3(ξ3) (here, ξ j , j = 1, 2, 3, are independent random variables with values in X and distributions μ j ; α j and β j are automorphisms of X) implies that either one, or two, or three of the distributions μ j are idempotents.

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Authors and Affiliations

  1. Angers University, France

    P. Graczyk

  2. Physicotechnical Institute of Low Temperatures, Ukrainian Academy of Sciences, Kharkov

    G. M. Fel'dman

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  1. P. Graczyk
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  2. G. M. Fel'dman
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Graczyk, P., Fel'dman, G.M. Independent Linear Statistics on Finite Abelian Groups. Ukrainian Mathematical Journal 53, 499–506 (2001). https://doi.org/10.1023/A:1012314302243

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