Том 71
№ 4

All Issues

Tolmacheva Yu. A.

Articles: 1
Article (Russian)

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

Tolmacheva Yu. A., Virchenko Yu. P.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2005. - 57, № 10. - pp. 1315–1326

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.