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Contact distribution in a thinned Boolean model with power-law radii

Part of: Stochastic processes Geometric probability and stochastic geometry

Published online by Cambridge University Press:  15 September 2017

Yinghua Dong  and
Gennady Samorodnitsky
Yinghua Dong*
Affiliation:
Nanjing University of Information Science and Technology
Gennady Samorodnitsky*
Affiliation:
Cornell University
*
* Postal address: College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, 210044, China. Email address: dongyinghua1@163.com
** Postal address: School of Operations Research and Information Engineering and Department of Statistical Science, Cornell University, Ithaca, NY 14853, USA. Email address: gs18@cornell.edu
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Abstract

We consider a weighted stationary spherical Boolean model in ℝd to which a Matérn-type thinning is applied. Assuming that the radii of the balls in the Boolean model have regularly varying tails, we establish the asymptotic behavior of the tail of the contact distribution of the thinned germ–grain model under four different thinning procedures of the original model.

Keywords

Boolean modelhard-core thinningpower tailcontact distributionempty space

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 60G57: Random measures
Type
Research Papers
Information
Journal of Applied Probability , Volume 54 , Issue 3 , September 2017 , pp. 670 - 684
Copyright
Copyright © Applied Probability Trust 2017 

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