INEQUALITIES FOR STATIONARY POISSON CUBOID PROCESSES

A cuboid is a rectangular parallelepipedon. By the notion ''stationary Poisson cuboid process'' we understand a stationary Poisson hyperplan e process which divides the Euclidean space R(d) into cuboids. It is e quivalent to speak of a stationary Poisson cuboid tessellation. The di stributions of volume and total edge length of the typical cuboid and the origin-cuboid of a stationary Poisson cuboid process are considere d. It is shown that these distributions become minimal, in the sense o f a specific order relation, in the case of quasi-isotropy. A possible connection to a more general problem, treated in [6], is also discuss ed.