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Mathematics > Probability

arXiv:1804.08740 (math)
[Submitted on 23 Apr 2018 (v1), last revised 30 Nov 2018 (this version, v2)]

Title:Splitting tessellations in spherical spaces

Authors:Daniel Hug, Christoph Thaele
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Abstract:The concept of splitting tessellations and splitting tessellation processes in spherical spaces of dimension $d\geq 2$ is introduced. Expectations, variances and covariances of spherical curvature measures induced by a splitting tessellation are studied using tools from spherical integral geometry. Also the spherical pair-correlation function of the $(d-1)$-dimensional Hausdorff measure is computed explicitly and compared to its analogue for Poisson great hypersphere tessellations. Finally, the typical cell distribution and the distribution of the typical spherical maximal face of any dimension $k\in\{1,\ldots,d-1\}$ are expressed as mixtures of the related distributions of Poisson great hypersphere tessellations. This in turn is used to determine the expected length and the precise birth time distribution of the typical maximal spherical segment of a splitting tessellation.
Subjects: Probability (math.PR); Metric Geometry (math.MG)
MSC classes: 52A22, 60D05, Secondary 53C65
Cite as: arXiv:1804.08740 [math.PR]
  (or arXiv:1804.08740v2 [math.PR] for this version)
  https://doi.org/10.48550/arXiv.1804.08740

Submission history

From: Christoph Thaele [view email]
[v1] Mon, 23 Apr 2018 21:15:21 UTC (248 KB)
[v2] Fri, 30 Nov 2018 14:11:54 UTC (267 KB)
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