CLT for Lipschitz-Killing curvatures of excursion sets of Gaussian random fields

Forthcoming (2017) in Journal of Theoretical ProbabilityOur interest in this paper is to explore limit theorems for various geometric function-als of excursion sets of isotropic Gaussian random fields. In the past, limit theorems have been proven for various geometric functionals of excursion sets/sojourn times (see [4, 13, 14, 18, 22, 25] for a sample of works in such settings). The most recent addition being [6] where a central limit theorem (CLT) for Euler-Poincaré characteristic of the excursions set of a Gaussian random field is proven under appropriate conditions. In this paper, we obtain a CLT for some global geometric functionals, called the Lipschitz-Killing curvatures of excursion sets of Gaussian random fields in an appropriate setting