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arxiv: math/0605035 · v1 · submitted 2006-05-01 · 🧮 math.PR · cond-mat.stat-mech· math-ph· math.MP

Two-Dimensional Critical Percolation: The Full Scaling Limit

Federico Camia , Charles M. Newman This is my paper
classification 🧮 math.PR cond-mat.stat-mechmath-phmath.MP
keywords limitprocessscalingcontinuumcriticalfullpercolationclusters
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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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  1. Three-point functions in critical loop models

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    Conjecture of an exact formula for 3-point functions of ℓ-leg and diagonal fields in critical loop models, supported by transfer-matrix numerics on cylinders that agree in most cases.