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Autre Publication Scientifique Année : 2011

Planar percolation with a glimpse of Schramm-Loewner Evolution

Résumé

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 $(p-1/2)_+^{5/36+o(1)}$ when $p$ approaches its critical value $p_c=1/2$.
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Dates et versions

ensl-00605057 , version 1 (30-06-2011)
ensl-00605057 , version 2 (01-11-2011)
ensl-00605057 , version 3 (07-06-2013)

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Vincent Beffara, Hugo Duminil-Copin. Planar percolation with a glimpse of Schramm-Loewner Evolution. 2011. ⟨ensl-00605057v2⟩
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