On the relationship between the 0-cell and the typical cell of a stationary random tessellation

✍ Scribed by J. Mecke

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 82 KB
• Volume: 32
• Category: Article
• ISSN: 0031-3203
• DOI: 10.1016/s0031-3203(99)00026-6

✦ Synopsis

The paper contains variations on the subject, `The 0-cell in a stationary random tessellation is in a sense larger than the typical cella. It is well-known that the mean volume of the 0-cell in a stationary random tessellation in the d-dimensional Euclidean space (d"1, 2, 2 ) is not smaller than the mean volume of the typical cell. It can be shown that a corresponding statement is true for all moments. By a suitable interpretation, it is possible to say that almost surely the volume of the typical cell is not greater than the volume of the 0-cell. In the case of Poisson hyperplane tessellation, it is even true that the typical cell can be imbedded as a subset in the 0-cell.