Department of statistics, Imam Khomeini international university
Abstract
The main goal of this paper is to investigate the site and bond percolation of the lattice Z2. The main symbols and concepts, including critical probabilities, are introduced. Bethe lattice and k-branching trees are examined and finally lattice Z2 is considered. ThefundamentaltheoremofHarrisandKestenthatpresentsthelowerandupperboundsofthecriticalprobability on the lattice Z2 expresses and proves.
