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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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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DOI: https://doi.org/10.1007/s00440-008-0183-5
Mathematics Subject Classification (2000)
- Primary: 37O35
- Secondary: 28D99
- 37A99
- 60K35
- 82B43