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September 2013 Hard-core thinnings of germ‒grain models with power-law grain sizes
Mikko Kuronen, Lasse Leskelä
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Adv. in Appl. Probab. 45(3): 595-625 (September 2013). DOI: 10.1239/aap/1377868531


Random sets with long-range dependence can be generated using a Boolean model with power-law grain sizes. We study thinnings of such Boolean models which have the hard-core property that no grains overlap in the resulting germ‒grain model. A fundamental question is whether long-range dependence is preserved under such thinnings. To answer this question, we study four natural thinnings of a Poisson germ‒grain model where the grains are spheres with a regularly varying size distribution. We show that a thinning which favors large grains preserves the slow correlation decay of the original model, whereas a thinning which favors small grains does not. Our most interesting finding concerns the case where only disjoint grains are retained, which corresponds to the well-known Matérn type-I thinning. In the resulting germ‒grain model, typical grains have exponentially small sizes, but rather surprisingly, the long-range dependence property is still present. As a byproduct, we obtain new mechanisms for generating homogeneous and isotropic random point configurations having a power-law correlation decay.


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Mikko Kuronen. Lasse Leskelä. "Hard-core thinnings of germ‒grain models with power-law grain sizes." Adv. in Appl. Probab. 45 (3) 595 - 625, September 2013.


Published: September 2013
First available in Project Euclid: 30 August 2013

zbMATH: 1282.60013
MathSciNet: MR3102464
Digital Object Identifier: 10.1239/aap/1377868531

Primary: 60D05
Secondary: 60G55

Rights: Copyright © 2013 Applied Probability Trust


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Vol.45 • No. 3 • September 2013
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