## Abstract

It was argued by Schramm and Smirnov that the critical site percolation exploration path on the triangular lattice converges in distribution to the trace of chordal SLE _{6}. We provide here a detailed proof, which relies on Smirnov's theorem that crossing probabilities have a conformally invariant scaling limit (given by Cardy's formula). The version of convergence to SLE _{6} that we prove suffices for the Smirnov-Werner derivation of certain critical percolation crossing exponents and for our analysis of the critical percolation full scaling limit as a process of continuum nonsimple loops.

Original language | English (US) |
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Pages (from-to) | 473-519 |

Number of pages | 47 |

Journal | Probability Theory and Related Fields |

Volume | 139 |

Issue number | 3-4 |

DOIs | |

State | Published - Nov 2007 |

## Keywords

- Conformal invariance
- Continuum scaling limit
- Critical behavior
- Percolation
- SLE
- Triangular lattice

## ASJC Scopus subject areas

- Analysis
- Statistics and Probability
- Statistics, Probability and Uncertainty

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