Two-Dimensional Critical Percolation: The Full Scaling Limit

Federico Camia; Charles M. Newman

doi:10.1007/s00220-006-0086-1

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Two-Dimensional Critical Percolation: The Full Scaling Limit

Federico Camia·Charles M. Newman

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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.

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BibTeX RIS

Federico Camia, Charles M. Newman. 2006-05-01. Two-Dimensional Critical Percolation: The Full Scaling Limit. https://doi.org/10.1007/s00220-006-0086-1

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