Splitting tessellations in spherical spaces

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...

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Bibliographic Details
Published in:arXiv.org 2018-11
Main Authors: Hug, Daniel, Thaele, Christoph
Format: Article
Language:English
Subjects:
Curvature
Hyperspheres
Splitting
Tessellation
Online Access:Get full text
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Summary: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.
ISSN:2331-8422