Mean Values of Weighted Cells of Stationary Poisson Hyperplane Tessellations of IRd
✍ Scribed by Wassilis Favis; Viola Weiß
- Publisher
- John Wiley and Sons
- Year
- 1998
- Tongue
- English
- Weight
- 530 KB
- Volume
- 193
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
✦ Synopsis
This paper deals with stationary Poisson hyperplane tessellations. Weighted distributions are considered, where the weights are the volume of the cell and the total volume of all faces of the cell. A randomly chosen cell according to such a weighted distribution will be called volume weighted cell and face content weighted cell, respectively. Mean values of cell characteristics for such weighted cells are calculated. These results are connected with second -order quantities for the typical cell of a stationary Poisson hyperplane tessellation. There are no suppositions to the isotropy of the tessellation, stationarity is sufficient. In case of isotropy already known results for planar tessellations from [AMS], [Mil] and [Mi21 will be confirmed. A stereological interpretation of weighted cells is given by the aid of suitable intersections.
1991 Mathematics Subject Classification. 60D05.