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We consider the Bernoulli Boolean discrete percolation model on thed-dimensional integer lattice. We study sufficient conditions on thedistribution of the radii of balls placed at the points of a Bernoulli pointprocess for the absence of percolation, provided that the intensity of theunderlying point process is small enough. We also study a Harris graphicalprocedure to construct, forward in time, particle systems with interactions ofinfinite range under the assumption that the corresponding generator admits aKalikow-type decomposition. We do so by using the subcriticality of the booleanmodel of discrete percolation.

Absence of percolation in the Bernoulli Boolean model