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Inequalities for Stationary Poisson Cuboid Processes

✍ Scribed by Wassilis Favis

Publisher
John Wiley and Sons
Year
1996
Tongue
English
Weight
465 KB
Volume
178
Category
Article
ISSN
0025-584X

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✦ Synopsis

A cuboid is a rectangular parallelepipedon. By the notion "stationary Poisson cuboid process" we understand a stationary Poisson hyperplane process which divides the Euclidean space Rd into cuboids. It is equivalent to speak of a stationary Poisson cuboid tessellation. The distributions of volume and total edge length of the typical cuboid and the origin-cuboid of a stationary Poisson cuboid process are considered. It is shown that these distributions become minimal, in the sense of a specific order relation, in the case of quasi-isotropy. A possible connection to a more general problem, treated in [6], is also discussed.

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