Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

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

Language

English

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. © 2011 Elsevier Inc.

Keywords

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

Publication Date

2011

Source Publication Title

Journal of Mathematical Analysis and Applications

Volume

384

Issue

2

Start Page

647

End Page

657

Publisher

Elsevier

DOI

10.1016/j.jmaa.2011.06.007

Link to Publisher's Edition

http://dx.doi.org/10.1016/j.jmaa.2011.06.007

ISSN (print)

0022247X

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