English

Anisotropic non-oriented bond percolation in high dimensions

Probability 2025-01-03 v2 Mathematical Physics math.MP

Abstract

We consider inhomogeneous non-oriented Bernoulli bond percolation on Zd\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.

Keywords

Cite

@article{arxiv.2106.09083,
  title  = {Anisotropic non-oriented bond percolation in high dimensions},
  author = {Pablo A. Gomes and Alan Pereira and Remy Sanchis},
  journal= {arXiv preprint arXiv:2106.09083},
  year   = {2025}
}

Comments

To appear in Journal of Theoretical Probability

R2 v1 2026-06-24T03:17:15.618Z