Random models for unions of balls

This project concerns random models for unions of d-dimensional balls.
The common model is a Boolean model, and we construct new models in terms of densities with respect to a Boolean model. For a finite union, the construction is rather straightforward; for an infinite union we consider a so-called local specification, i.e. certain conditional densities. The densities are used to model various
geometric properties of finite unions of balls, including volume, surface area, edge length,number of vertices, number of voids (or equivalently the Euler characteristic); also geometric properties of the voids will be modelled. The
computations will be based on some useful inclusion-exclusion formulas.