The lowest crossing in 2D critical percolation
Probability
2011-01-10 v1 Mathematical Physics
math.MP
Abstract
We study the following problem for critical site percolation on the triangular lattice. Let A and B be sites on a horizontal line e separated by distance n. Consider, in the half-plane above e, the lowest occupied crossing R from the half-line left of A to the half-line right of B. We show that the probability that R has a site at distance smaller than m from AB is of order (log (n/m))^{-1}, uniformly in 1 <= m < n/2. Much of our analysis can be carried out for other two-dimensional lattices as well.
Keywords
Cite
@article{arxiv.math/0201030,
title = {The lowest crossing in 2D critical percolation},
author = {J. van den Berg and A. A. Jarai},
journal= {arXiv preprint arXiv:math/0201030},
year = {2011}
}
Comments
16 pages, Latex, 2 eps figures, special macros: percmac.tex. Submitted to Annals of Probability