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

Abstract : 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.
Type de document :
Pré-publication, Document de travail
MAP5 2017-30. 2018
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Contributeur : Raphael Lachieze-Rey <>
Soumis le : jeudi 13 décembre 2018 - 17:51:16
Dernière modification le : vendredi 1 février 2019 - 15:50:13


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  • HAL Id : hal-01654056, version 3
  • ARXIV : 1712.01558



Raphaël Lachieze-Rey. Normal convergence of non-localised geometric functionals and shot noise excursions. MAP5 2017-30. 2018. 〈hal-01654056v3〉



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