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Faces with given directions in anisotropic Poisson hyperplane mosaics
| Content Provider | Scilit |
|---|---|
| Author | Hug, Daniel Schneider, Rolf |
| Copyright Year | 2011 |
| Description | 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. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/7E86B34C6B8FB0D9EA994C0D146FFBD2/S0001867800004869a.pdf/div-class-title-faces-with-given-directions-in-anisotropic-poisson-hyperplane-mosaics-div.pdf |
| Ending Page | 321 |
| Page Count | 14 |
| Starting Page | 308 |
| ISSN | 00018678 |
| e-ISSN | 14756064 |
| DOI | 10.1017/s0001867800004869 |
| Journal | Advances in Applied Probability |
| Issue Number | 02 |
| Volume Number | 43 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 2011-06-01 |
| Access Restriction | Open |
| Subject Keyword | Advances in Applied Probability Interdisciplinary Mathematics Poisson Hyperplane Tessellation weighted Typical Face Typical Face Conditional Distribution Blaschke Body |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Statistics and Probability |
