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

  • Yu. P. Virchenko
  • Yu. A. Tolmacheva


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.

How to Cite
Virchenko, Y. P., and Y. A. Tolmacheva. “Majorant Estimates for the Percolation Threshold of a Bernoulli Field on a Square Lattice”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, no. 10, Oct. 2005, pp. 1315–1326,
Research articles