Equivalence of the void percolation problem for overlapping spheres and a network problem

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Abstract
The percolation problem for the complement of the union of randomly located, overlapping spheres is shown to be equivalent to a bond percolation problem on the edges of the Voronoi tesselation of the sphere centres. This result provides a convenient definition of cluster size, and therefore of the critical exponents, for this problem. It also provides an efficient algorithm for Monte Carlo computation of the percolation threshold and the critical exponents.