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Introduction to site and bond percolation on the lattice $mathbb{Z}^2$
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Ramin KAZEMI *   |
| Imam Khomeini international university |
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Abstract: (2081 Views) |
The main goal of this paper is to investigate the site and bond percolation of the lattice $mathbb{Z}^2$. The main symbols and concepts, including critical probabilities, are introduced. Bethe lattice and $k$-branching trees are examined and finally lattice
$mathbb{Z}^2$ is considered. The fundamental theorem of Harris and Kesten that presents the lower and upper bounds of the critical probability on the lattice $mathbb{Z}^2$ expresses and proves. |
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| Keywords: Site and bond percolation, critical probabilities, lattice $mathbb{Z}^2$. |
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Full-Text [PDF 778 kb]
(913 Downloads)
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Type of Study: Research |
Subject:
Special
Received: 2021/07/25 | Accepted: 2021/11/22 | Published: 2021/12/1
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