Grain rotations and distortions in the asymptotic variance of vacancy of the Boolean model

Christian Rau*, Sung Nok CHIU

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We consider the asymptotic variance of vacancy (AVV) in the high intensity small-grain Boolean model. Subjecting the grains to rotations or, more generally, linear distortions gives rise to a function which maps distortion distributions to the AVV of the corresponding Boolean model. We mainly study continuity properties of this function, where we use the L1 Wasserstein metric on distortion distributions. An important role in the formulation and derivation of our results is played by notions of symmetry commonly used in multivariate analysis and stochastic simulation, such as conjugation-invariance and group models.

Original languageEnglish
Pages (from-to)647-657
Number of pages11
JournalJournal of Mathematical Analysis and Applications
Volume384
Issue number2
DOIs
Publication statusPublished - 15 Dec 2011

Scopus Subject Areas

  • Analysis
  • Applied Mathematics

User-Defined Keywords

  • Boolean model
  • Coverage
  • Rotations
  • Set covariance function
  • Vacancy
  • Wasserstein distance

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