Percolation and $O(1)$ loop model
Probability
2021-12-01 v1 Mathematical Physics
Complex Variables
math.MP
Abstract
We present an "ultimate" proof of Cardy's formula for the critical percolation on the hexagonal lattice \cite{Smirnov01criticalpercolation}, showing the existence of the universal and conformally invariant scaling limit of crossing probabilities. The new approach is more conceptual, less technically demanding, and is amenable to generalizations.
Keywords
Cite
@article{arxiv.2111.15612,
title = {Percolation and $O(1)$ loop model},
author = {Mikhail Khristoforov and Stanislav Smirnov},
journal= {arXiv preprint arXiv:2111.15612},
year = {2021}
}
Comments
9 pages, 4 figures