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<p>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.</p>

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APPROXIMATIONS OF THE PERCOLATION PROBABILITY ON THE PERIODIC GRAPH \(\mathbb {Z}^2\)

  • 期刊论文

  • 发表日期：

    2025年10月1日

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  • Yu. P. Virchenko,
  • D. A. Cherkashin

摘要

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.