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Percolation on the three dot system
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  • Published: 30 October 2008

Percolation on the three dot system

  • J.-F. Quint1 

Probability Theory and Related Fields volume 146, Article number: 49 (2010) Cite this article

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Abstract

Let \({X\subset(\mathbb Z/2\mathbb Z)^{\mathbb Z^2}}\) be the three dot system. Given a \({\mathbb Z^2}\) -invariant ergodic probability measure on X, we study percolation properties on the set of 1’s in a typical orbit. This gives us a strong dichotomy for such measures.

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References

  1. Burton R.M., Keane M.: Density and uniqueness in percolation. Commun. Math. Phys. 121, 501–505 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  2. Einsiedler M.: Invariant subsets and invariant measures for irreducible actions on zero-dimensional groups. Bull. Lond. Math. Soc. 36, 321–331 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  3. Fürstenberg H.: Disjointness in ergodic theory, minimal sets, and a problem in Diophantine approximation. Math. Syst. Theory 1, 1–49 (1967)

    Article  Google Scholar 

  4. Host B., Maass A., Martínez S.: Uniform Bernoulli measure in dynamics of permutative cellular automata with algebraic local rules. Discrete Continuous Dyn. Syst. 9, 1423–1446 (2003)

    Article  MATH  Google Scholar 

  5. Ledrappier F.: Un champ markovien peut ê d’entropie nulle et mélangeant. Comptes-rendus de l’Acad. Sci. 287, 561–563 (1978)

    MATH  MathSciNet  Google Scholar 

  6. Sablik, M.: Measure rigidity for algebraic bipermutative cellular automata (preprint)

  7. Silberger S.: Subshifts of the three dot system. Ergodic Theory Dyn. Syst. 25, 1673–1687 (2005)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. LAGA, Université Paris 13, 99, avenue Jean-Baptiste Clément, 93430, Villetaneuse, France

    J.-F. Quint

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  1. J.-F. Quint
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Correspondence to J.-F. Quint.

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Quint, JF. Percolation on the three dot system. Probab. Theory Relat. Fields 146, 49 (2010). https://doi.org/10.1007/s00440-008-0183-5

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  • Received: 17 July 2008

  • Revised: 08 September 2008

  • Published: 30 October 2008

  • DOI: https://doi.org/10.1007/s00440-008-0183-5

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Mathematics Subject Classification (2000)

  • Primary: 37O35
  • Secondary: 28D99
  • 37A99
  • 60K35
  • 82B43
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