Anisotropic Non-oriented Bond Percolation in High Dimensions

Pablo A. Gomes (), Alan Pereira () and Remy Sanchis ()
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Pablo A. Gomes: Universidade de São Paulo
Alan Pereira: Universidade Federal de Alagoas
Remy Sanchis: Universidade Federal de Minas Gerais

Journal of Theoretical Probability, 2024, vol. 37, issue 1, 121-132

Abstract: Abstract We consider inhomogeneous non-oriented Bernoulli bond percolation on $$\mathbb {Z}^d$$ 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: Anisotropic percolation; Bond percolation; High dimensional systems; Coupling; Phase diagram; 60K35; 82B43 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10959-023-01254-9

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