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Process level moderate deviations for stabilizing functionals

Published online by Cambridge University Press:  07 October 2008

Peter Eichelsbacher
Fakultät für Mathematik, Ruhr-Universität Bochum, NA 3/68, 44780 Bochum, Germany;
Tomasz Schreiber
Faculty of Mathematics and Computer Science, Nicholas Copernicus University, Toruń, Poland;
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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. 

Research Article
© EDP Sciences, SMAI, 2010

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