Some Exceptional Conngurations

The Dirichlet form given by the intrinsic gradient on Poisson space is associated with a Markov process consisting of a countable family of interacting diiusions. By considering each diiusion as a particle with unit mass, the randomly evolving connguration can be thought of as a Radon measure valued diiusion. The quasi-sure analysis of Dirichlet forms is used to nd exceptional sets for this Markov process. We show that the process never hits certain unusual conngurations, such as those with more than unit mass at some position, or those that violate the law of large numbers. Some of these results also hold for Gibbs measures with superstable interactions.