  Given a Gibbs point process $\P^{\Psi}$ on $\R^d$ having a weak enough
potential $\Psi$, we consider the random measures $\mu_\la := \sum_{x \in
\P^{\Psi} \cap Q_\la} \xi(x, \P^{\Psi} \cap Q_\la) \delta_{x/\la^{1/d}}$, where
$Q_{\la} := [-\la^{1/d}/2,\la^{1/d}/2]^d$ is the volume $\la$ cube and where
$\xi(\cdot,\cdot)$ is a translation invariant stabilizing functional. Subject
to $\Psi$ satisfying a localization property and translation invariance, we
establish weak laws of large numbers for $\la^{-1} \mu_\la(f)$, $f$ a bounded
test function on $\R^d$, and weak convergence of $\la^{-1/2} \mu_\la(f),$
suitably centered, to a Gaussian field acting on bounded test functions. The
result yields limit laws for geometric functionals on Gibbs point processes
including the Strauss and area interaction point processes as well as more
general point processes defined by the Widom-Rowlinson and hard-core model. We
provide applications to random sequential packing on Gibbsian input, to
functionals of Euclidean graphs, networks, and percolation models on Gibbsian
input, and to quantization via Gibbsian input.
