Two-Dimensional Critical Percolation: The Full Scaling Limit

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.

45 pages, 12 figures. This is a revised version of math.PR/0504036 without the appendices

References in corpus (2)

• Critical Percolation in Finite Geometries
• Path Crossing Exponents and the External Perimeter in 2D Percolation

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