Advances in Applied Probability
- Adv. in Appl. Probab.
- Volume 45, Number 3 (2013), 595-625.
Hard-core thinnings of germ‒grain models with power-law grain sizes
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.
Adv. in Appl. Probab., Volume 45, Number 3 (2013), 595-625.
First available in Project Euclid: 30 August 2013
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]
Secondary: 60G55: Point processes
Kuronen, Mikko; Leskelä, Lasse. Hard-core thinnings of germ‒grain models with power-law grain sizes. Adv. in Appl. Probab. 45 (2013), no. 3, 595--625. doi:10.1239/aap/1377868531. https://projecteuclid.org/euclid.aap/1377868531