*Tid:* **16 maj 2013 kl 14.15-15.00.**
**Seminarierummet 3721**, Institutionen för
matematik, KTH, Lindstedts väg 25, plan 7.
Karta!
*Föredragshållare:*
**
University Lecturer Lasse
Leskelä, Department of Mathematics and Statistics, University of Jyväskylä.
**
**Titel:**
Hard-core thinnings of germ–grain models with power-law grain sizes
**Abstract**
Random sets with long-range dependence can be generated using a Boolean
model with power-law grain sizes. This talk focuses on 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 Matérn-type thinnings of a Poisson germ–grain
model where the grains are spheres with a regularly varying size
distribution. It turns out 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. The most interesting
finding concerns the case where only disjoint grains are retained, which
corresponds to the 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. This talk is based on a paper with the same title
(arXiv:1204.1208), joint
work with Mikko
Kuronen (U Jyväskylä).
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