2017
Том 69
№ 6

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Majorant estimates for the percolation threshold of a Bernoulli field on a square lattice

Tolmacheva Yu. A., Virchenko Yu. P.

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Abstract

We suggest a method for obtaining a monotonically decreasing sequence of upper bounds of percolation threshold of the Bernoulli random field on $Z^2$. On the basis of this sequence, we obtain a method of constructing approximations with the guaranteed exactness estimate for a percolation probability. We compute the first term $c_2 = 0,74683$ of the considered sequence.

English version (Springer): Ukrainian Mathematical Journal 57 (2005), no. 10, pp 1535-1549.

Citation Example: Tolmacheva Yu. A., Virchenko Yu. P. Majorant estimates for the percolation threshold of a Bernoulli field on a square lattice // Ukr. Mat. Zh. - 2005. - 57, № 10. - pp. 1315–1326.

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