Crabgrass, Measles, and Gypsy Moths: An Introduction to Interacting Particle Systems*

Our aim in this paper is to explain some of the results about interacting particle systems to someone who has no knowledge of probability theory but unders tands w h a t it means to flip a coin wi th a probabili ty p of heads. In what follows we will discuss five models. The last three are h inted at in the title. The first two are simpler systems that will be useful in explaining the others. then ~n is the set of wet sites on level n when there is a source of fluid at (0,0). The model above is appropriate (if somewhat oversimplified) if one is thinking about the movemen t of oil in the ground pulled down by the force of gravity. With the last interpretation in mind, it is natural to ask if the material is porous enough for the fluid to penetrate it, or (letting P denote probability) "Is P(~, ~ 0 for all n) > 0?" When ~ ~ 0 for all