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A Percolating Hard Sphere Model

Codina Cotar·Alexander E. Holroyd·David Revelle
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Abstract

Given a homogeneous Poisson point process in R^d, Haggstrom and Meester asked whether it is possible to place spheres (of differing radii) centred at the points, in a translation-invariant way, so that the spheres do not overlap but there is an unbounded component of touching spheres. We prove that the answer is yes in sufficiently high dimension.

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Codina Cotar, Alexander E. Holroyd, David Revelle. 2006-07-25. A Percolating Hard Sphere Model. https://arxiv.org/abs/math/0607645

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