The Full Scaling Limit of Two-Dimensional Critical Percolation

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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. In the main body of the paper these results are proved while assuming, as argued by Schramm and Smirnov, that the percolation exploration path converges in distribution to the trace of chordal SLE(6). Then, in a lengthy appendix, a detailed proof is provided for this convergence to SLE(6), which itself relies on Smirnov's result that crossing probabilities converge to Cardy's formula.
67 pages, 22 figures

Keywords

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

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/74773

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0504036
 http://arxiv.org/abs/math/0504036

Collections

arXiv