A Percolating Hard Sphere Model

Details A Percolating Hard Sphere Model A Percolating Hard Sphere Model

2006-07-25

arxiv.org/abs/math/0607645v1

Mathematics

Probability

20 pages, 2 figures

Scientific paper

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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