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 $p\searrow p_c=1/2$.

Survey based on lectures given in "La Pietra week in Probability", Florence, Italy, 2011. (2013)

References in corpus (2)

• Bond percolation on isoradial graphs: criticality and universality
• Universality for bond percolation in two dimensions

Cited by in corpus (2)

• Percolation since Saint-Flour
• Limit of the Wulff Crystal when approaching criticality for site percolation on the triangular lattice