A Percolating Hard Sphere Model
Given a homogeneous Poisson point process in R(d), Haggstrom and Meester (Random Struct Algorithms 9 (1996) 295-315) 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. (C) 2008 Wiley Periodicals, Inc. Random Struct. Alg., 34, 285-299, 2009
percolation hard sphere model boolean model poisson process