  The purpose of the present paper is to establish explicit bounds on moderate
deviation probabilities for a rather general class of geometric functionals
enjoying the stabilization property, under Poisson input and the assumption of
a certain control over the growth of the moments of the functional and its
radius of stabilization. Our proof techniques rely on cumulant expansions and
cluster measures and yield completely explicit bounds on deviation
probabilities. In addition, we establish a new criterion for the limiting
variance to be non-degenerate. Moreover, our main result provides a new central
limit theorem, which, though stated under strong moment assumptions, does not
require bounded support of the intensity of the Poisson input. We apply our
results to three groups of examples: random packing models, geometric
functionals based on Euclidean nearest neighbors and the sphere of influence
graphs.
