## Planar percolation with a glimpse of Schramm-Loewner evolution.(English)Zbl 1283.60118

Summary: 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 the Schramm-Loewner evolution and techniques developed over the years in percolation, allows 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 $$(p-p_{c})^{5/36+o(1)}= 1/2$$ as $$p\searrow p_{c}$$.

### MSC:

 60K35 Interacting random processes; statistical mechanics type models; percolation theory 60J67 Stochastic (Schramm-)Loewner evolution (SLE)

### Keywords:

site percolation; critical phenomenon; conformal invariance
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