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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 $(p-1/2)_+^{5/36+o(1)}$ when $p$ approaches its critical value $p_c=1/2$.
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https://hal-ens-lyon.archives-ouvertes.fr/ensl-00605057
Contributor : Vincent Beffara <>
Submitted on : Tuesday, November 1, 2011 - 2:47:47 PM
Last modification on : Thursday, January 11, 2018 - 6:12:31 AM
Long-term archiving on: : Thursday, February 2, 2012 - 9:25:42 AM

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  • HAL Id : ensl-00605057, version 2
  • ARXIV : 1107.0158

Citation

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

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