  In this paper we present a detailed and exact study of the probability
density function $P(F)$ of the total force $F$ acting on a point particle
belonging to a perturbed lattice of identical point sources of a power law pair
interaction. The main results concern the large $F$ tail of $P(F)$ for which
two cases are mainly distinguished: (i) Gaussian-like fast decreasing $P(F)$
for lattice with perturbations forbidding any pair of particles to be found
arbitrarily close to one each other; (ii) L\'evy-like power law decreasing
$P(F)$ when this possibility is instead permitted. It is important to note that
in the second case the exponent of the power law tail of $P(F)$ is the same for
all perturbation (apart from very singular cases), and is in an one to one
correspondence with the exponent characterizing the behavior of the pair
interaction with the distance between the two particles.
