### 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) |
---|---|

Pages (from-to) | 311-332 |

Number of pages | 22 |

Journal | Communications in Mathematical Physics |

Volume | 246 |

Issue number | 2 |

DOIs | |

State | Published - Apr 2004 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Communications in Mathematical Physics*,

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

**A Particular Bit of Universality : Scaling Limits of Some Dependent Percolation Models.** / Camia, Federico; Newman, Charles; Sidoravicius, Vladas.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 246, no. 2, pp. 311-332. https://doi.org/10.1007/s00220-004-1042-6

}

TY - JOUR

T1 - A Particular Bit of Universality

T2 - Scaling Limits of Some Dependent Percolation Models

AU - Camia, Federico

AU - Newman, Charles

AU - Sidoravicius, Vladas

PY - 2004/4

Y1 - 2004/4

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=2142651448&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=2142651448&partnerID=8YFLogxK

U2 - 10.1007/s00220-004-1042-6

DO - 10.1007/s00220-004-1042-6

M3 - Article

VL - 246

SP - 311

EP - 332

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 2

ER -