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arXiv · 2106.09083

Anisotropic non-oriented bond percolation in high dimensions

Pablo A. Gomes·Alan Pereira·Remy Sanchis
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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.

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Pablo A. Gomes, Alan Pereira, Remy Sanchis. 2021-06-16. Anisotropic non-oriented bond percolation in high dimensions. https://doi.org/10.1007/s10959-023-01254-9

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