Process level moderate deviations for stabilizing functionals

¹ Fakultät für Mathematik, Ruhr-Universität Bochum, NA 3/68, 44780 Bochum, Germany; peter.eichelsbacher@ruhr-uni-bochum.de
² Faculty of Mathematics and Computer Science, Nicholas Copernicus University, Toruń, Poland; tomeks@mat.uni.torun.pl

Received: 26 November 2007
Revised: 25 January 2008

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 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.