Two-Dimensional Critical Percolation: The Full Scaling Limit

Federico Camia, Charles M. Newman

Published 2006-05-01Version 1

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.