Hierarchical models in discrete percolation theory and Markov branching processes

A brief introduction to percolation theory is given. Within the framework of the discrete percolation theory on infinite graphs, we develop a method for approximating the percolation probability based on the construction of a sequence of infinite graphs of a special type called the hierarchical graphs. The calculation of the percolation probability for graphs of this type is reduced to the analysis of a suitable Markov branching process with discrete time.