Geodesic
Estimates of critical probabilities of percolation on finite square grids
Journal of the Belarusian State University. Mathematics and Informatics, Tome 3 (2023), pp. 92-97

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In this paper, we investigate the problem of determining the critical probabilities of percolation for finite square grids. Basing on the Harris – Kesten theorem on critical probability $p_{c} (\mathbb{Z}^{2})$ in the infinite square grid, we prove that the exact threshold of exponential decay in the infinite square grid is equal to $\frac{1}{2}$. With the help of the evaluated value of $p_{g} (\mathbb{Z}^{2})$ we show that the critical probabilities of percolation on finite square grids are arbitrarily close to $\frac{1}{2}$ when the size of a grid is large enough.
Keywords: Percolation; critical probability; grid. 
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     title = {Estimates of critical probabilities of percolation on finite square grids},
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M. M. Vas'kovskii; A. O. Zadorozhnuyk; A. D. Dosova. Estimates of critical probabilities of percolation on finite square grids. Journal of the Belarusian State University. Mathematics and Informatics, Tome 3 (2023), pp. 92-97. http://geodesic.mathdoc.fr/item/BGUMI_2023_3_a8/