Anisotropic oriented percolation in high dimensions

Abstract

In this paper we study anisotropic oriented percolation on ${\mathbb{Z}}^d$ for $d\ge 4$ and show that the local condition for phase transition is closely related to the mean-field condition. More precisely, we show that if the sum of the local probabilities is strictly greater than one and each probability is not too large, then percolation occurs.

16 pages, without figures, revised version

References in corpus (1)

• Dimensional Crossover in Anisotropic Percolation on $Z^{d+s}$

Cited by in corpus (2)

• Anisotropic non-oriented bond percolation in high dimensions
• Upper bounds for critical probabilities in Bernoulli Percolation models