Vertex Numbers of Weighted Faces in Poisson Hyperplane Mosaics

In the random mosaic generated by a stationary Poisson hyperplane process in Rd , we consider the typical k-face weighted by the j-dimensional volume of the j-skeleton (0 j k d). We prove sharp lower and upper bounds for its expected number of vertices.

• Type: Journal
• Year: 2010
• Where: DCG
• Authors: Rolf Schneider
• Keywords: DCG 2010, J-dimensional Volume, Stationary Poisson Hyperplane, Typical K-face