  We consider the Bernoulli Boolean discrete percolation model on the
d-dimensional integer lattice. We study sufficient conditions on the
distribution of the radii of balls placed at the points of a Bernoulli point
process for the absence of percolation, provided that the intensity of the
underlying point process is small enough. We also study a Harris graphical
procedure to construct, forward in time, particle systems with interactions of
infinite range under the assumption that the corresponding generator admits a
Kalikow-type decomposition. We do so by using the subcriticality of the boolean
model of discrete percolation.
