A SUPPORT PROPERTY FOR INFINITE DIMENSIONAL INTERACTING DIFFUSION PROCESSES

UNE PROPRIÉTÉ DE SUPPORT POUR DES PROCESSUS DE DIFFUSION EN DIMENSION INFINIE AVEC INTERACTION.

MICHAEL RÖCKNER BYRON SCHMULAND

Abstract. The Dirichlet form associated with the intrinsic gradient on Poisson space is known to be quasi-regular on the complete metric space Γ̈ = {Z_{+}-valued Radon measures on IR^{d}}. We show that under mild conditions, the set Γ̈ \ Γ is E-exceptional, where Γ is the space of locally finite configurations in IR^{d}, that is, measures γ ∈ Γ̈ satisfying sup_{x∈IR^{d}} γ({x}) ≤ 1. Thus, the associated diffusion lives on the smaller space Γ. This result also holds for Gibbs measures with superstable interactions.