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2013 Planar percolation with a glimpse of Schramm–Loewner evolution
Vincent Beffara, Hugo Duminil-Copin
Probab. Surveys 10: 1-50 (2013). DOI: 10.1214/11-PS186


In recent years, important progress has been made in the field of two-dimensional statistical physics. One of the most striking achievements is the proof of the Cardy–Smirnov formula. This theorem, together with the introduction of Schramm–Loewner Evolution and techniques developed over the years in percolation, allow precise descriptions of the critical and near-critical regimes of the model. This survey aims to describe the different steps leading to the proof that the infinite-cluster density $\theta(p)$ for site percolation on the triangular lattice behaves like $(p-p_{c})^{5/36+o(1)}$ as $p\searrow p_{c}=1/2$.


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Vincent Beffara. Hugo Duminil-Copin. "Planar percolation with a glimpse of Schramm–Loewner evolution." Probab. Surveys 10 1 - 50, 2013.


Published: 2013
First available in Project Euclid: 20 September 2013

zbMATH: 1283.60118
MathSciNet: MR3161674
Digital Object Identifier: 10.1214/11-PS186

Keywords: conformal invariance , critical phenomenon , site percolation

Rights: Copyright © 2013 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.10 • 2013
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