In:
Advances in Applied Probability, Cambridge University Press (CUP), Vol. 43, No. 02 ( 2011-06), p. 308-321
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 & lt; 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.
Type of Medium:
Online Resource
ISSN:
0001-8678
,
1475-6064
DOI:
10.1017/S0001867800004869
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
2011
detail.hit.zdb_id:
1474602-5
