Planar percolation with a glimpse of Schramm-Loewner Evolution

Abstract : 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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Submitted on : Friday, June 7, 2013 - 10:44:58 AM
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Vincent Beffara, Hugo Duminil-Copin. Planar percolation with a glimpse of Schramm-Loewner Evolution. Probability Surveys, Institute of Mathematical Statistics (IMS), 2013, 10, pp.1-50. ⟨10.1214/11-PS186⟩. ⟨ensl-00605057v3⟩

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