On the distribution of the spherical contact vector of stationary germ-grain models

@article{Last1998OnTD,
  title={On the distribution of the spherical contact vector of stationary germ-grain models},
  author={Guenter Last and Rolf Schassberger},
  journal={Advances in Applied Probability},
  year={1998},
  volume={30},
  pages={36 - 52}
}
We consider a stationary germ-grain model Ξ with convex and compact grains and the distance r(x) from x ε ℝ d to Ξ. For almost all points x ε ℝ d there exists a unique point p(x) in the boundary of Ξ such that r(x) is the length of the vector x-p(x), which is called the spherical contact vector at x. In this paper we relate the distribution of the spherical contact vector to the times it takes a typical boundary point of Ξ to hit another grain if all grains start growing at the same time and at… 
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