A Central Limit Theorem for Lipschitz-Killing Curvatures of Gaussian Excursions

Dennis Müller

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arXiv · 1607.06696

A Central Limit Theorem for Lipschitz-Killing Curvatures of Gaussian Excursions

Dennis Müller

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Abstract

This paper studies the excursion set of a real stationary isotropic Gaussian random field above a fixed level. We show that the standardized Lipschitz-Killing curvatures of the intersection of the excursion set with a window converges in distribution to a normal distribution as the window grows to the $d$-dimensional Euclidean space. Moreover a lower bound for the asymptotic variance is shown.

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Dennis Müller. 2016-07-22. A Central Limit Theorem for Lipschitz-Killing Curvatures of Gaussian Excursions. https://arxiv.org/abs/1607.06696

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