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

• Date: 2005
• Main Authors: Virchenko, Yu. P., Tolmacheva, Yu. A., Вирченко, Ю. П., Толмачева, Ю. А.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2005
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3687
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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...