Anisotropic non-oriented bond percolation in high dimensions

Abstract

We consider inhomogeneous non-oriented Bernoulli bond percolation on ${\mathbb{Z}}^d$, where each edge has a parameter depending on its direction. We prove that, under certain conditions, if the sum of the parameters is strictly greater than 1/2, we have percolation in sufficiently high dimensions. The main tool is a dynamical coupling between models for different dimensions with different sets of parameters.

To appear in Journal of Theoretical Probability

References in corpus (2)

• A note on the dimensional crossover critical exponent
• Anisotropic oriented percolation in high dimensions

Cited by in corpus (1)

• Upper bounds for critical probabilities in Bernoulli Percolation models