arXiv:math/0611116 Abstract

arXiv:math/0611116 [math.PR]Abstract References Reviews Resources

SLE(6) and CLE(6) from Critical Percolation

Published 2006-11-05Version 1

We review some of the recent progress on the scaling limit of two-dimensional critical percolation; in particular, the convergence of the exploration path to chordal SLE(6) and the "full" scaling limit of cluster interface loops. The results given here on the full scaling limit and its conformal invariance extend those presented previously. For site percolation on the triangular lattice, the results are fully rigorous. We explain some of the main ideas, skipping most technical details.

Comments: 23 pages, 6 figures

Categories: math.PR, cond-mat.stat-mech, math-ph, math.MP

Subjects: 82B27, 60K35, 82B43, 60D05, 30C35

Keywords: conformal invariance extend, cluster interface loops, exploration path, chordal sle, two-dimensional critical percolation

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