Two-Dimensional Critical Percolation: The Full Scaling Limit
Probability
2009-11-11 v1 Statistical Mechanics
Mathematical Physics
math.MP
Abstract
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.
Cite
@article{arxiv.math/0605035,
title = {Two-Dimensional Critical Percolation: The Full Scaling Limit},
author = {Federico Camia and Charles M. Newman},
journal= {arXiv preprint arXiv:math/0605035},
year = {2009}
}
Comments
45 pages, 12 figures. This is a revised version of math.PR/0504036 without the appendices