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Process level moderate deviations for stabilizing functionals

Peter Eichelsbacher·Tomasz Schreiber
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Abstract

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.

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Peter Eichelsbacher, Tomasz Schreiber. 2006-03-16. Process level moderate deviations for stabilizing functionals. https://arxiv.org/abs/math/0603402

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