Planar percolation with a glimpse of SchrammLoewner Evolution
Abstract
In recent years, important progress has been made in the field of twodimensional statistical physics. One of the most striking achievements is the proof of the CardySmirnov formula. This theorem, together with the introduction of SchrammLoewner Evolution and techniques developed over the years in percolation, allow precise descriptions of the critical and nearcritical regimes of the model. This survey aims to describe the different steps leading to the proof that the infinitecluster density $\theta(p)$ for site percolation on the triangular lattice behaves like $(pp_c)^{5/36+o(1)}$ as $p\searrow p_c=1/2$.
 Publication:

arXiv eprints
 Pub Date:
 July 2011
 DOI:
 10.48550/arXiv.1107.0158
 arXiv:
 arXiv:1107.0158
 Bibcode:
 2011arXiv1107.0158B
 Keywords:

 Mathematics  Probability;
 Condensed Matter  Statistical Mechanics
 EPrint:
 Survey based on lectures given in "La Pietra week in Probability", Florence, Italy, 2011. (2013)