Estimates of critical probabilities of percolation on finite square grids

Authors

  • Maksim M. Vaskouski Belarusian State University, 4 Niezaliezhnasci Avenue, Minsk 220030, Belarus
  • Anna O. Zadorozhnyuk EPAM Systems, 1 Akademika Kuprevicha Street, 1 building, Minsk 220141, Belarus
  • Anna D. Dosova EPAM Systems, 1 Akademika Kuprevicha Street, 1 building, Minsk 220141, Belarus

Keywords:

percolation, critical probability, grid

Abstract

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 pc(Z2) in the infinite square grid, we prove that the exact threshold of exponential decay in the infinite square grid is equal to 1/2. With the help of the evaluated value of pg(Z2) we show that the critical probabilities of percolation on finite square grids are arbitrarily close to 1/2 when the size of a grid is large enough.

Author Biographies

  • Maksim M. Vaskouski, Belarusian State University, 4 Niezaliezhnasci Avenue, Minsk 220030, Belarus

    doctor of science (physics and mathematics), full professor; head of the department of higher mathematics, faculty of applied mathematics and computer science

     

  • Anna O. Zadorozhnyuk, EPAM Systems, 1 Akademika Kuprevicha Street, 1 building, Minsk 220141, Belarus

    assistant at the department of higher mathematics, faculty of applied mathematics and computer science

     

  • Anna D. Dosova, EPAM Systems, 1 Akademika Kuprevicha Street, 1 building, Minsk 220141, Belarus

    system analyst

     

References

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Published

2023-12-13

Issue

No. 3 (2023): Journal of the Belarusian State University. Mathematics and Informatics

Section

Short Communications

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How to Cite

[1]
Vaskouski, M.M. et al. 2023. Estimates of critical probabilities of percolation on finite square grids. Journal of the Belarusian State University. Mathematics and Informatics. 3 (Dec. 2023), 92–97.