Hyperplane and Particle Processes

As we want to consider random hyperplane processes and the systems of polytopes in the tessellations they induce, we shall need random processes of different kinds of geometric objects. For this reason, we first recall the notion of a general point process, where the ‘points’ are elements of a suitable topological space. Then we introduce processes of flats, in particular hyperplanes, and processes of convex particles. These are then used to model the cells of a random hyperplane tessellation.