Almost sure behavior of functionals of stationary Gibbs point processes

This paper is concerned with the almost sure control of functionals of stationary Gibbs point processes. We apply Kahane-Khintchine's inequality to derive an almost sure control of various functionals under very mild assumption on the spatial point process X. In particular, if X is a locally stable Gibbs point process with finite range observed in [-n, n](d), we obtain the bound N-[-n,N-n]d (X)/(2n)(d) = rho + O-a.s. (n(-d/2) log n(3/2)) as n -> infinity, where N-w (X) is the number of points of X boolean AND W for W subset of R-d and where rho is the intensity parameter of X. (C) 2014 Elsevier B.V. All rights reserved.