Source: Adv. in Appl. Probab. Volume 37, Number 3
(2005), 604-628.
We consider a hard-sphere model in ℝd generated by a stationary point process N
and the lilypond growth
protocol: at time 0, every point of N starts growing with unit speed in all directions to form a system of
balls in
which any particular ball ceases its growth at the instant that it collides with another ball. Some quite general
conditions are given, under which it is shown that the model is well defined and exhibits no percolation. The absence
of percolation is attributable to the fact that, under our assumptions, there can be no descending chains in
N. The proof of this fact forms a significant part of the paper. It is also shown that, in the absence of
descending
chains, mutual-nearest-neighbour matching can be used to construct a bijective point map as defined by Thorisson.
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