Oriented Percolation in One-Dimensional 1/|x-y|^2 Percolation Models
概率论
2013-04-26 v3 数学物理
math.MP
摘要
We consider independent edge percolation models on Z, with edge occupation probabilities p_<x,y> = p if |x-y| = 1, 1 - exp{- beta / |x-y|^2} otherwise. We prove that oriented percolation occurs when beta > 1 provided p is chosen sufficiently close to 1, answering a question posed in [Commun. Math. Phys. 104, 547 (1986)]. The proof is based on multi-scale analysis.
引用
@article{arxiv.math/0506404,
title = {Oriented Percolation in One-Dimensional 1/|x-y|^2 Percolation Models},
author = {D. H. U. Marchetti and V. Sidoravicius and M. E. Vares},
journal= {arXiv preprint arXiv:math/0506404},
year = {2013}
}
备注
19 pages, 2 figures. See also Commentary on J. Stat. Phys. 150, 804-805 (2013), DOI 10.1007/s10955-013-0702-3