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Second Order Analysis of Geometric Functionals of Boolean Models

  • Daniel Hug
  • Michael A. Klatt
  • Günter Last
  • Matthias Schulte
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2177)

Abstract

This chapter presents asymptotic covariance formulae and central limit theorems for geometric functionals, including volume, surface area, and all Minkowski functionals and translation invariant Minkowski tensors as prominent examples, of stationary Boolean models. Special focus is put on the anisotropic case. In the (anisotropic) example of aligned rectangles, we provide explicit analytic formulae and compare them with simulation results. We discuss which information about the grain distribution second moments add to the mean values.

Notes

Acknowledgements

We would like to thank Julia Schulte and Klaus Mecke for some helpful remarks and discussions. The authors were supported by the German Research Foundation (DFG) through the research unit “Geometry and Physics of Spatial Random Systems”.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Daniel Hug
    • 1
  • Michael A. Klatt
    • 1
  • Günter Last
    • 1
  • Matthias Schulte
    • 2
  1. 1.Department of MathematicsKarlsruhe Institute of TechnologyKarlsruheGermany
  2. 2.Department of Mathematics and Statistics, Institute of Mathematical Statistics and Actuarial ScienceUniversity of BernBernSwitzerland

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