Asymptotics of the visibility function in the Boolean model

Abstract : The aim of this paper is to give a precise estimate on the tail probability of the visibility function in a germ-grain model: this function is defined as the length of the longest ray starting at the origin that does not intersect an obstacle in a Boolean model. We proceed in two or more dimensions using coverage techniques. Moreover, convergence results involving a type I extreme value distribution are shown in the two particular cases of small obstacles or a large obstacle-free region.
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Submitted on : Tuesday, January 4, 2011 - 10:56:31 PM
Last modification on : Tuesday, November 19, 2019 - 10:28:21 AM
Long-term archiving on: Tuesday, April 5, 2011 - 3:14:25 AM

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  • HAL Id : hal-00389798, version 2
  • ARXIV : 0905.4874

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Pierre Calka, Julien Michel, Sylvain Porret-Blanc. Asymptotics of the visibility function in the Boolean model. 2009. ⟨hal-00389798v2⟩

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