Oriented Percolation in One-Dimensional 1/|x-y|^2 Percolation Models
Marchetti, D. H. U. ; Sidoravicius, V. ; Vares, M. E.
arXiv, 0506404 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2005-06-20
Classification:  Mathematics - Probability,  Mathematical Physics,  82B43, 82B20, 60K35 
@article{0506404,
     author = {Marchetti, D. H. U. and Sidoravicius, V. and Vares, M. E.},
     title = {Oriented Percolation in One-Dimensional 1/|x-y|^2 Percolation Models},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0506404}
}

Marchetti, D. H. U.; Sidoravicius, V.; Vares, M. E. Oriented Percolation in One-Dimensional 1/|x-y|^2 Percolation Models. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0506404/