Critical percolation in the plane
Probability
2009-09-27 v1 Mathematical Physics
Complex Variables
math.MP
Abstract
We study scaling limits and conformal invariance of critical site percolation on triangular lattice. We show that some percolation-related quantities are harmonic conformal invariants, and calculate their values in the scaling limit. As a particular case we obtain conformal invariance of the crossing probabilities and Cardy's formula. Then we prove existence, uniqueness, and conformal invariance of the continuum scaling limit.
Keywords
Cite
@article{arxiv.0909.4499,
title = {Critical percolation in the plane},
author = {Stanislav Smirnov},
journal= {arXiv preprint arXiv:0909.4499},
year = {2009}
}
Comments
This is a copy of an old preprint from 2001, which I will perhaps update in the future