Process level moderate deviations for stabilizing functionals

Issue		ESAIM: PS Volume 14, 2010


Page(s)		1 - 15
DOI		10.1051/ps:2008027
Published online		11 February 2010

ESAIM: PS, February 2010, Vol. 14, p. 1-15

Process level moderate deviations for stabilizing functionals

Peter Eichelsbacher¹ and Tomasz Schreiber²

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.  

Mathematics Subject Classification: 60F05 / 60D05

Key words: Moderate deviations / random Euclidean graphs / random sequential packing.

What is OpenURL?

The OpenURL standard is a protocol for transmission of metadata describing the resource that you wish to access. An OpenURL link contains article metadata and directs it to the OpenURL server of your choice. The OpenURL server can provide access to the resource and also offer complementary services (specific search engine, export of references...). The OpenURL link can be generated by different means.

If your librarian has set up your subscription with an OpenURL resolver, OpenURL links appear automatically on the abstract pages.
You can define your own OpenURL resolver with your EDPS Account. In this case your choice will be given priority over that of your library.
You can use an add-on for your browser (Firefox or I.E.) to display OpenURL links on a page (see http://www.openly.com/openurlref/). You should disable this module if you wish to use the OpenURL server that you or your library have defined.