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Two-Dimensional Critical Percolation: The Full Scaling Limit
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.Comment: 45 pages, 12 figures. This is a revised version of math.PR/0504036
without the appendice
One-arm exponent for critical 2D percolation
The probability that the cluster of the origin in critical site percolation
on the triangular grid has diameter larger than is proved to decay like
as
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