Approximations of the percolation probability on a periodic graph $\mathbb{Z}^2$
- Authors: Virchenko Y.P.1, Cherkashin D.A.1
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Affiliations:
- Belgorod Shukhov State Technological University
- Issue: Vol 242 (2025)
- Pages: 22-40
- Section: Articles
- URL: https://ogarev-online.ru/2782-4438/article/view/312569
- DOI: https://doi.org/10.36535/2782-4438-2025-242-22-40
- ID: 312569
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Abstract
A method for constructing approximations of arbitrarily high accuracy for the probability of percolation from a fixed vertex on a square lattice is developed. Based on this method, a first approximation of the percolation probability is calculated, which gives a guaranteed upper estimate for it together with a lower bound for the percolation threshold.
About the authors
Yuri Petrovich Virchenko
Belgorod Shukhov State Technological UniversityDoctor of physico-mathematical sciences, Professor
Dmitrii Andreevich Cherkashin
Belgorod Shukhov State Technological University
References
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