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

We propose a method for obtaining a monotonically decreasing sequence of upper bounds of the percolation threshold of a Bernoulli random field on ℤ². On the basis of this sequence, we develop a method for the construction of approximations with guaranteed exactness estimate for the percolation probability. The first term of the sequence is calculated (c ₂ = 0.74683). __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 10, pp. 1315–1326, October, 2005.