ABSTRACT
This chapter considers a large system of interacting particles evolving in time, one of the natural things is to provide a simplified description of the state of the system. Rather than provide a detailed “microscopic” picture, the chapter describes the system by providing the values of certain “macroscopic” parameters. The model considered in the chapter describes particles on sites in a d-dimensional periodic lattice. Particles may jump at some Poisson rates to nearby sites if any of them should be vacant. The Poisson rate could depend on the immediate environment of the current particle. This would of course happen simultaneously for all the particles. Although locally the system will be changing fast, the local “density” of particles will change rather slowly because no particles are created or destroyed. Assuming that density is the only conserved quantity there will be an one parameter family of invariant measures for the evolution.
