Critical percolation exploration path and SLE 6 : a proof of convergence

@inproceedings{Camia2006CriticalPE,
  title={Critical percolation exploration path and SLE 6 : a proof of convergence},
  author={Federico Camia and Charles M. Newman},
  year={2006}
}
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 SLE6. 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 SLE6 that we prove suffices for the Smirnov–Werner derivation of certain critical percolation crossing exponents and for our… CONTINUE READING

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