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A condition for distinguishing sceneries on non-abelian groups

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  • Hildebrand, Martin

Abstract

A scenery f on a finite group G is a function from G to {0,1}. A random walk v(t) on G is said to be able to distinguish two sceneries if the distributions of the sceneries evaluated on the random walk with uniform initial distribution are identical only if one scenery is a shift of the other scenery. This paper generalizes a sufficient condition of Finucane, Tamuz, and Yaari for distinguishing two sceneries on finite abelian groups to one for finite non-abelian groups but shows that no random walks on finite non-abelian groups satisfy this sufficient condition.

Suggested Citation

  • Hildebrand, Martin, 2017. "A condition for distinguishing sceneries on non-abelian groups," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2339-2345.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:7:p:2339-2345
    DOI: 10.1016/j.spa.2016.11.001
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    References listed on IDEAS

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    1. Matzinger, Heinrich & Lember, Jüri, 2006. "Reconstruction of periodic sceneries seen along a random walk," Stochastic Processes and their Applications, Elsevier, vol. 116(11), pages 1584-1599, November.
    2. Keane, M. & den Hollander, W.Th.F., 1986. "Ergodic properties of color records," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 138(1), pages 183-193.
    3. Finucane, Hilary & Tamuz, Omer & Yaari, Yariv, 2014. "Scenery reconstruction on finite abelian groups," Stochastic Processes and their Applications, Elsevier, vol. 124(8), pages 2754-2770.
    Full references (including those not matched with items on IDEAS)

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