Weitzenböck Formulas on Poisson Probability Spaces

Abstract

This paper surveys and compares some recent approaches to stochastic infinite-dimensional geometry on the space $\Gamma$ of configurations (i. e. locally finite subsets) of a Riemannian manifold $M$ under Poisson measures. In particular, different approaches to Bochner–Weitzenböck formulas are considered. A unitary transform is also introduced by mapping functions of $n$ configuration points to their multiple stochastic integral.