RT - Journal Article T1 - Introduction to site and bond percolation on the lattice $mathbb{Z}^2‎$ JF - Andishe-_ye-Amari YR - 2021 JO - Andishe-_ye-Amari VO - 26 IS - 1 UR - http://andisheyeamari.irstat.ir/article-1-863-en.html SP - 61 EP - 70 K1 - Site and bond percolation K1 - critical probabilities K1 - lattice $mathbb{Z}^2‎$. AB - 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. LA eng UL http://andisheyeamari.irstat.ir/article-1-863-en.html M3 ER -