Abstract
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.
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Hug, D., Schneider, R. Typical Cells in Poisson Hyperplane Tessellations. Discrete Comput Geom 38, 305–319 (2007). https://doi.org/10.1007/s00454-007-1340-9
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DOI: https://doi.org/10.1007/s00454-007-1340-9