Typical Cells in Poisson Hyperplane Tessellations

It is proved that the shape of the typical cell of a stationary and isotropic Poisson random hyperplane tessellation is, with high probability, close to the shape of a ball if the kth intrinsic volume (k ≥ 2) of the typical cell is large. The shape of typical cells of large diameter is close to the shape of a segment.

• Type: Journal
• Year: 2007
• Where: DCG
• Authors: Daniel Hug, Rolf Schneider
• Keywords: DCG 2007, Kth Intrinsic Volume, Poisson Random Hyperplane, Typical Cells