Contact distribution in a thinned Boolean model with power law radii

We consider a weighted stationary spherical Boolean model in R^d. Assuming that the radii of the balls in the Boolean model have regularly varying tails, we establish the asymptotic behaviour of the tail of the contact distribution of the thinned germ-grain model under 4 different thinning procedures of the original model.Dong's research was partially supported by Jiangsu Planned Projects for Postdoctoral Research Funds (No. 1501053A) , the Statistical Scientific Research Program of National Bureau of Statistics of China (No. 2015LY83) and the foundation of Nanjing University of Information Science and Technology (No. 2014x026). Samorodnitsky's research was partially supported by the ARO grant W911NF-12-10385 and by the NSF grant DMS-1506783 at Cornell University