Hodge theory for a certain class of non-compact manifolds

The Hodge theorem provides a canonical choice of representatives for DeRham cohomology. His original theory applies to compact manifolds and relies on resolvent estimates which seem to require compactness. In this lecture I will explain how his theory can be extended to a class of non-compact manifolds which are sufficiently trivial at infinity. The basic analytic tool is an estimate which holds when Brownian motion is subjected to a very strong centripetal force field.