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June 2011 Faces with given directions in anisotropic Poisson hyperplane mosaics
Daniel Hug, Rolf Schneider
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Adv. in Appl. Probab. 43(2): 308-321 (June 2011).

Abstract

For stationary Poisson hyperplane tessellations in d-dimensional Euclidean space and a dimension k ∈ {1, ..., d}, we investigate the typical k-face and the weighted typical k-face (weighted by k-dimensional volume), without isotropy assumptions on the tessellation. The case k = d concerns the previously studied typical cell and zero cell, respectively. For k < d, we first find the conditional distribution of the typical k-face or weighted typical k-face, given its direction. Then we investigate how the shapes of the faces are influenced by assumptions of different types: either via containment of convex bodies of given volume (including a new result for k = d), or, for weighted typical k-faces, in the spirit of D. G. Kendall's asymptotic problem, suitably generalized. In all these results on typical or weighted typical k-faces with given direction space L, the Blaschke body of the section process of the underlying hyperplane process with L plays a crucial role.

Citation

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Daniel Hug. Rolf Schneider. "Faces with given directions in anisotropic Poisson hyperplane mosaics." Adv. in Appl. Probab. 43 (2) 308 - 321, June 2011.

Information

Published: June 2011
First available in Project Euclid: 21 June 2011

zbMATH: 1234.60013
MathSciNet: MR2848377

Subjects:
Primary: 60D05

Rights: Copyright © 2011 Applied Probability Trust

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Vol.43 • No. 2 • June 2011
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