Open Access
2011 Conformally invariant scaling limits in planar critical percolation
Nike Sun
Probab. Surveys 8: 155-209 (2011). DOI: 10.1214/11-PS180


This is an introductory account of the emergence of conformal invariance in the scaling limit of planar critical percolation. We give an exposition of Smirnov’s theorem (2001) on the conformal invariance of crossing probabilities in site percolation on the triangular lattice. We also give an introductory account of Schramm-Loewner evolutions (SLEκ), a one-parameter family of conformally invariant random curves discovered by Schramm (2000). The article is organized around the aim of proving the result, due to Smirnov (2001) and to Camia and Newman (2007), that the percolation exploration path converges in the scaling limit to chordal SLE6. No prior knowledge is assumed beyond some general complex analysis and probability theory.


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Nike Sun. "Conformally invariant scaling limits in planar critical percolation." Probab. Surveys 8 155 - 209, 2011.


Published: 2011
First available in Project Euclid: 28 October 2011

zbMATH: 1245.60096
MathSciNet: MR2846901
Digital Object Identifier: 10.1214/11-PS180

Primary: 30C35 , 60K35
Secondary: 60J65

Keywords: Conformally invariant scaling limits , percolation , percolation exploration path , preharmonicity , preholomorphicity , Schramm-Loewner Evolutions

Rights: Copyright © 2011 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.8 • 2011
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