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 , 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.
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