Percolation theory deals with these and related questions, and was motivated by the need for simple but clarifying models of cooperative phenomena like the spread of infection in a population, or a gas through a porous medium.
A random spatial process (e.g., the process describing which nodes in a communication network are busy, or which spins in a magnetic material are `up' or `down') is called mixing if, roughly speaking, knowledge of the state of a given vertex gives almost no information about the states of remote vertices. Mixing is closely related to stability.
We will explain how percolation methods, combined with so-called coupling arguments, are useful in the study of mixing properties of an important class of models.
The emphasis of this talk is on intuitive ideas rather than mathematical formalism.