Critical Percolation Exploration Path and SLE(6): a Proof of Convergence

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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.
45 pages, 14 figures; revised version following the comments of a referee

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Probability, Mathematical Physics, 82B27, 60K35, 82B43, 60D05, 30C35

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http://salesiana.dossiersoluciones.com/handle/123456789/111658

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0604487
 http://arxiv.org/abs/math/0604487

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arXiv