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May 2010 Large faces in Poisson hyperplane mosaics
Daniel Hug, Rolf Schneider
Ann. Probab. 38(3): 1320-1344 (May 2010). DOI: 10.1214/09-AOP510


A generalized version of a well-known problem of D. G. Kendall states that the zero cell of a stationary Poisson hyperplane tessellation in ℝd, under the condition that it has large volume, approximates with high probability a certain definite shape, which is determined by the directional distribution of the underlying hyperplane process. This result is extended here to typical k-faces of the tessellation, for k∈{2, …, d−1}. This requires the additional condition that the direction of the face be in a sufficiently small neighbourhood of a given direction.


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Daniel Hug. Rolf Schneider. "Large faces in Poisson hyperplane mosaics." Ann. Probab. 38 (3) 1320 - 1344, May 2010.


Published: May 2010
First available in Project Euclid: 2 June 2010

zbMATH: 1202.60021
MathSciNet: MR2675001
Digital Object Identifier: 10.1214/09-AOP510

Primary: 60D05
Secondary: 52A20

Keywords: D. G. Kendall’s problem , limit shape , Poisson hyperplane tessellation , volume-weighted typical face

Rights: Copyright © 2010 Institute of Mathematical Statistics


Vol.38 • No. 3 • May 2010
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