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

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dc.creatorCamia, Federico
dc.creatorNewman, Charles M.
dc.date2006-04-22
dc.date2006-11-07
dc.date.accessioned2026-07-07T07:11:11Z
dc.date.available2026-07-07T07:11:11Z
dc.descriptionIt 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.
dc.description45 pages, 14 figures; revised version following the comments of a referee
dc.identifierhttps://arxiv.org/abs/math/0604487
dc.identifierhttp://arxiv.org/abs/math/0604487
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/111658
dc.subjectProbability
dc.subjectMathematical Physics
dc.subject82B27, 60K35, 82B43, 60D05, 30C35
dc.titleCritical Percolation Exploration Path and SLE(6): a Proof of Convergence
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