Elements of Percolation Theory

In contrast to many other modern research fronts, percolation theory is a problem that is, in principle, easy to define (8-13). In general, a percolation model is a collection of points (or sites) distributed in space, certain 

There are many percolation models (11,13). The most typical and important ones are discussed in the following sections. 

In this model, the vertices of a lattice (i.e., sites) rather than its edges are blocked, i.e., each site is declared to be open with the probability q and is 

In the framework of this model, both the edges and the vertices of a regular lattice may be open or closed, with different probabilities. The lattice 

The Bethe lattice (or tree) is a lattice containing no closed loops (see, e.g., Fig. 6). The latter results in a simple analytical solution of the bond and site problems for these lattices. In addition, the general percolation properties for Bethe and regular lattices are often close. For these reasons, the Bethe lattices are rather popular in applied science publications, although these lattices have no physical sense. 

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