Weighted faces of Poisson hyperplane tessellations
Schneider Rolf
Source: Adv. in Appl. Probab.
Volume 41, Number 3
(2009), 682-694.
Abstract
We study lower-dimensional volume-weighted typical faces of a
stationary Poisson hyperplane tessellation in d-dimensional
Euclidean space. After showing how their distribution can be
derived from that of the zero cell, we obtain sharp lower and
upper bounds for the expected vertex number of the volume-weighted
typical k-face (k=2,...,d). The bounds are respectively
attained by parallel mosaics and by isotropic tessellations. We
conclude with a remark on expected face numbers and expected
intrinsic volumes of the zero cell.
Primary Subjects: 60D05
Secondary Subjects: 60G55
Keywords: Poisson hyperplane tessellation; volume-weighted typical face; Palm distribution; extremal vertex number; parallel mosaic; associated zonoid; volume product
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aap/1253281060
Digital Object Identifier: doi:10.1239/aap/1253281060
Zentralblatt MATH identifier:
05625064
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