A Percolating Hard Sphere Model
Codina Cotar, Alexander E. Holroyd, David Revelle
Abstract
Given a homogeneous Poisson point process in Rd, 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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