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

Normal convergence of non-localised geometric functionals and shot noise excursions