Percolation

Percolation is the first spatial model we will consider. The model is very easy to define but not so easy to analyze. This is why this chapter will not be self-contained. For harder results, we will refer to G. Grimmett (1999). Elementary methods can, however, be used to prove a number of results and give a taste of percolation. We will use combinatorics, discrete branching processes, and coupling techniques.