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.