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Convergence of percolation probability functions to cumulative distribution functions on square lattices with (1,0)-neighborhood

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  • Moskalev, P.V.

Abstract

We consider a percolation model on square lattices with sites weighted by beta-distributed random variables S∼Beta(a,b) with a positive real parameters a>0 and b>0. Using the Monte Carlo method, we estimate the percolation probability P∞ as a relative frequency P∞∗ averaged over the target subset of sites on a square lattice. As a result of the comparative analysis, we formulate two empirical hypotheses: the first on the correspondence of percolation thresholds pc to p0-quantiles (where level p0=0.592746… coincides with the percolation threshold for the site percolation model on a square lattice) of random variables Si weighing sites of the square lattice, and the second on the convergence of statistical estimates of percolation probability functions P∞∗(p) to cumulative distribution functions FSi(p) of these variables Si for the supercritical values of the occupation probability p≥pc.

Suggested Citation

  • Moskalev, P.V., 2020. "Convergence of percolation probability functions to cumulative distribution functions on square lattices with (1,0)-neighborhood," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).
    • Handle: RePEc:eee:phsmap:v:553:y:2020:i:c:s0378437120303216
    DOI: 10.1016/j.physa.2020.124657
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