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Scenery reconstruction on finite abelian groups

Author

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  • Finucane, Hilary
  • Tamuz, Omer
  • Yaari, Yariv

Abstract

We consider the question of when a random walk on a finite abelian group with a given step distribution can be used to reconstruct a binary labeling of the elements of the group, up to a shift. Matzinger and Lember (2006) give a sufficient condition for reconstructability on cycles. While, as we show, this condition is not in general necessary, our main result is that it is necessary when the length of the cycle is prime and larger than 5, and the step distribution has only rational probabilities. We extend this result to other abelian groups.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:8:p:2754-2770
    DOI: 10.1016/j.spa.2014.03.012
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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. Matzinger, Heinrich & Rolles, Silke W. W., 2003. "Reconstructing a piece of scenery with polynomially many observations," Stochastic Processes and their Applications, Elsevier, vol. 107(2), pages 289-300, October.
    3. Howard, C. Douglas, 1997. "Distinguishing certain random sceneries on ##Z## via random walks," Statistics & Probability Letters, Elsevier, vol. 34(2), pages 123-132, June.
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    Cited by:

    1. Hildebrand, Martin, 2017. "A condition for distinguishing sceneries on non-abelian groups," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2339-2345.

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