Stochastic analysis with the gamma measure—Moving a dense set

The Gamma measure corresponds to a measure on a marked configuration space with an infinite measure on the marks. We construct Dirichlet forms for the movement of marks and positions. These include the movement of the support, which is a dense set in $\mathbb {R}^d$, $d \in \mathbb {N}$. The key ingredient is a recently discovered integration by parts formula for the directional derivative w.r.t. the positions. We briefly introduce the geometry and then concentrate on the construction of the Dirichlet forms.