Process level moderate deviations for stabilizing functionals
Fakultät für Mathematik, Ruhr-Universität Bochum, NA 3/68, 44780 Bochum, Germany; firstname.lastname@example.org
2 Faculty of Mathematics and Computer Science, Nicholas Copernicus University, Toruń, Poland; email@example.com
Revised: 25 January 2008
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 is 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.
Mathematics Subject Classification: 60F05 / 60D05
Key words: Moderate deviations / random Euclidean graphs / random sequential packing.
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