### Abstract

We use SLE _{6} paths to construct a process of continuum nonsimple loops in the plane and prove that this process coincides with the full continuum scaling limit of 2D critical site percolation on the triangular lattice - that is, the scaling limit of the set of all interfaces between different clusters. Some properties of the loop process, including conformal invariance, are also proved.

Original language | English (US) |
---|---|

Pages (from-to) | 1-38 |

Number of pages | 38 |

Journal | Communications in Mathematical Physics |

Volume | 268 |

Issue number | 1 |

DOIs | |

State | Published - Nov 2006 |

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### ASJC Scopus subject areas

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

### Cite this

**Two-dimensional critical percolation : The full scaling limit.** / Camia, Federico; Newman, Charles.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 268, no. 1, pp. 1-38. https://doi.org/10.1007/s00220-006-0086-1

}

TY - JOUR

T1 - Two-dimensional critical percolation

T2 - The full scaling limit

AU - Camia, Federico

AU - Newman, Charles

PY - 2006/11

Y1 - 2006/11

N2 - We use SLE 6 paths to construct a process of continuum nonsimple loops in the plane and prove that this process coincides with the full continuum scaling limit of 2D critical site percolation on the triangular lattice - that is, the scaling limit of the set of all interfaces between different clusters. Some properties of the loop process, including conformal invariance, are also proved.

AB - We use SLE 6 paths to construct a process of continuum nonsimple loops in the plane and prove that this process coincides with the full continuum scaling limit of 2D critical site percolation on the triangular lattice - that is, the scaling limit of the set of all interfaces between different clusters. Some properties of the loop process, including conformal invariance, are also proved.

UR - http://www.scopus.com/inward/record.url?scp=33749356449&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33749356449&partnerID=8YFLogxK

U2 - 10.1007/s00220-006-0086-1

DO - 10.1007/s00220-006-0086-1

M3 - Article

VL - 268

SP - 1

EP - 38

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -