Anisotropic Non-oriented Bond Percolation in High Dimensions

Anisotropic Non-oriented Bond Percolation in High Dimensions

We consider inhomogeneous non-oriented Bernoulli bond percolation on 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 too...

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Veröffentlicht in:Journal of theoretical probability 2024-03, Vol.37 (1), p.121-132
Hauptverfasser: Gomes, Pablo A., Pereira, Alan, Sanchis, Remy
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics
Mathematics and Statistics
Parameters
Percolation
Probability Theory and Stochastic Processes
Statistics
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Zusammenfassung:We consider inhomogeneous non-oriented Bernoulli bond percolation on 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.
ISSN:0894-9840
1572-9230
DOI:10.1007/s10959-023-01254-9