### Abstract

We study families of dependent site percolation models on the triangular lattice double struck T sign and hexagonal lattice ℍ that arise by applying certain cellular automata to independent percolation configurations. We analyze the scaling limit of such models and show that the distance between macroscopic portions of cluster boundaries of any two percolation models within one of our families goes to zero almost surely in the scaling limit. It follows that each of these cellular automaton generated dependent percolation models has the same scaling limit (in the sense of Aizenman-Burchard [3]) as independent site percolation on double struck T sign.

Original language | English (US) |
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Pages (from-to) | 311-332 |

Number of pages | 22 |

Journal | Communications In Mathematical Physics |

Volume | 246 |

Issue number | 2 |

DOIs | |

State | Published - Apr 2004 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

*Communications In Mathematical Physics*,

*246*(2), 311-332. https://doi.org/10.1007/s00220-004-1042-6