2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115126Given 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.20 pages, 2 figuresProbability60K35; 60D05; 60G55text