Mixing and Ergodicity

For a stationary particle process (with convex particles) with a locally finite intensity measure, the density of, for example, an intrinsic volume can be defined by averaging over all realizations of the particle process. In some cases, it may be possible to obtain the same density from a single realization, by only a spatial averaging. More precisely, this will be possible if the particle process is ergodic, or has the stronger roperty of being mixing. In the present apter, we deal with such properties for stationary Poisson hyperplane processes and tessellations.