Crossing probabilities for planar percolation
Abstract
We prove a general RussoSeymourWelsh 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.
 Publication:

arXiv eprints
 Pub Date:
 November 2020
 arXiv:
 arXiv:2011.04618
 Bibcode:
 2020arXiv201104618K
 Keywords:

 Mathematics  Probability;
 Mathematical Physics;
 primary: 60K35;
 secondary: 82B43;
 68Q87
 EPrint:
 25 pages, 16 figures