Stochastic analysis on product manifolds: Dirichlet operators on differential forms

We define a de Rham complex over a product manifold (infinite product of co mpact manifolds), and Dirichlet operators on differential Forms, associated with differentiable measures (in particular, Gibbs measures), which genera lize the notions of Bochner and de Rham Laplacians. We give probabilistic r epresentations for corresponding semigroups and study properties of the cor responding; stochastic dynamics. (C) 2000 Academic Press.