Recent Results on Finite and Infinite SysteIlls of Interacting Diffusions

Abstract

We review some recent results concerning the long time behavior of finite and infinite systems of interacting diffusions. After presenting the basic ergodic theory of the infinite systems, we observe that the long time behavior of the finite systems differs drastically from that of the infinite system, at least from a naive point of view. A theorem comparing the finit.e and infinite systems on different time scales is presented which gives a more complete picture of what is going on.