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Random Johnson-Mehl tessellations

Part of: Geometric probability and stochastic geometry Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Jesper Møller
Jesper Møller*
Affiliation:
University of Aarhus
*
∗Postal address: Department of Theoretical Statistics, Institute of Mathematics, University of Aarhus, DK-8000 Aarhus C, Denmark.
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Abstract

A unified exposition of random Johnson–Mehl tessellations in d-dimensional Euclidean space is presented. In particular, Johnson-Mehl tessellations generated by time-inhomogeneous Poisson processes and nucleation-exclusion models are studied. The ‘practical' cases d = 2 and d = 3 are discussed in detail. Several new results are established, including first- and second-order moments of various characteristics for both Johnson–Mehl tesselations and sectional Johnson–Mehl tessellations.

Keywords

CRYSTAL CHARACTERISTICSHARD CORE PROCESSESINHOMOGENEOUS POISSON PROCESSESMEAN VALUE RELATIONSNUCLEATION–EXCLUSION MODELPALM DISTRIBUTIONRANDOM TESSELLATIONSSECTIONAL TESSELLATIONSSPATIAL BIRTH PROCESSESSTEREOLOGYSTOCHASTIC GEOMETRYVORONOI TESSELLATIONS

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 60G55: Point processes
Type
Research Article
Information
Advances in Applied Probability , Volume 24 , Issue 4 , December 1992 , pp. 814 - 844
Copyright
Copyright © Applied Probability Trust 1992 

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