Percolation without FKG
Probability
2018-04-09 v2 Mathematical Physics
math.MP
Abstract
We prove a Russo-Seymour-Welsh theorem for large and natural perturbative families of discrete percolation models that do not necessarily satisfy the Fortuin-Kasteleyn-Ginibre condition of positive association. In particular, we prove the box-crossing property for the antiferromagnetic Ising model with small parameter, and for certain discrete Gaussian fields with oscillating correlation function.
Cite
@article{arxiv.1710.10644,
title = {Percolation without FKG},
author = {Vincent Beffara and Damien Gayet},
journal= {arXiv preprint arXiv:1710.10644},
year = {2018}
}