Process level moderate deviations for stabilizing functionals

Functionals of spatial point process often satisfy a weak spatial dependence condition known as stabilization. In this paper we prove process level moderate deviation principles (MDP) for such functionals, which are a level-3 result for empirical point fields as well as a level-2 result for empirical point measures. The level-3 rate function coincides with the so-called specific information. We show that the general result can be applied to prove MDPs for various particular functionals, including random sequential packing, birth-growth models, germ-grain models and nearest neighbor graphs.