  This article presents a complete second order theory for a large class of
geometric functionals on homogeneous Poisson input. In particular, the results
don't require the existence of a radius of stabilisation. Hence they can be
applied to geometric functionals of spatial shot-noise fields excursions such
as volume, perimeter, or Euler characteristic (the method still applies to
stabilising functionals). More generally, it must be checked that a local
contribution to the functional is not strongly affected under a perturbation of
the input far away. In this case the exact asymptotic variance is given, as
well as the likely optimal speed of convergence in the central limit theorem.
This goes through a general mixing-type condition that adapts nicely to both
proving asymptotic normality and that variance is of volume order.
