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Intersections of random sets
Published online by Cambridge University Press: 17 January 2022
Abstract
We consider a variant of a classical coverage process, the Boolean model in
$\mathbb{R}^d$
. Previous efforts have focused on convergence of the unoccupied region containing the origin to a well-studied limit C. We study the intersection of sets centered at points of a Poisson point process confined to the unit ball. Using a coupling between the intersection model and the original Boolean model, we show that the scaled intersection converges weakly to the same limit C. Along the way, we present some tools for studying statistics of a class of intersection models.
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- © The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust
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