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arXiv · 1107.0158

Planar percolation with a glimpse of Schramm-Loewner Evolution

Vincent Beffara·Hugo Duminil-Copin
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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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Vincent Beffara, Hugo Duminil-Copin. 2011-07-01. Planar percolation with a glimpse of Schramm-Loewner Evolution. https://arxiv.org/abs/1107.0158

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