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

2006/11/05 by Camia, Federico, Newman, Charles M. · 2 citations
#30C35 #60D05 #60K35 #82B27 #82B43 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.math/0611116

Abstract

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.

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• Liouville quantum gravity: from random planar maps to conformal field theory
• Random walk reflected off of infinity, with applications to uniform spanning forests and supercritical Liouville quantum gravity

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