:: Volume 26, Issue 1 (12-2021) ::
Andishe 2021, 26(1): 61-70 Back to browse issues page
Introduction to site and bond percolation on the lattice $mathbb{Z}^2‎$
Ramin KAZEMI *
Imam Khomeini international university
Abstract:   (1510 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.

Keywords: Site and bond percolation, critical probabilities, lattice $mathbb{Z}^2‎$.
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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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Volume 26, Issue 1 (12-2021) Back to browse issues page