0506404 (D. H. U. Marchetti et al.)

Oriented Percolation in One-Dimensional 1/|x-y|^2 Percolation Models    [PDF]

D. H. U. Marchetti, V. Sidoravicius, M. E. Vares

We consider independent edge percolation models on Z, with edge occupation probabilities p_ = 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.

View original: http://arxiv.org/abs/0506404