Crossing probabilities for planar percolation
Probability
2020-11-10 v1 Mathematical Physics
math.MP
Abstract
We prove a general Russo-Seymour-Welsh result valid for any invariant planar percolation process satisfying positive association. This means that the probability of crossing a rectangle in the long direction is related by a homeomorphism to the probability of crossing it in the short direction. This homeomorphism is universal in the sense that it depends only on the aspect ratio of the rectangle, and is uniform in the scale and the considered model.
Keywords
Cite
@article{arxiv.2011.04618,
title = {Crossing probabilities for planar percolation},
author = {Laurin Köhler-Schindler and Vincent Tassion},
journal= {arXiv preprint arXiv:2011.04618},
year = {2020}
}
Comments
25 pages, 16 figures