Almost Sure Central Limit Theorems in Stochastic Geometry

Giovanni-Luca Torrisi; Emilio Leonardi

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arXiv · 1912.06503

Almost Sure Central Limit Theorems in Stochastic Geometry

Giovanni-Luca Torrisi·Emilio Leonardi

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Abstract

We prove an almost sure central limit theorem on the Poisson space, which is perfectly tailored for stabilizing functionals emerging in stochastic geometry. As a consequence, we provide almost sure central limit theorems for $(i)$ the total edge length of the $k$-nearest neighbors random graph, $(ii)$ the clique count in random geometric graphs, $(iii)$ the volume of the set approximation via the Poisson-Voronoi tessellation.

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Giovanni-Luca Torrisi, Emilio Leonardi. 2019-12-13. Almost Sure Central Limit Theorems in Stochastic Geometry. https://arxiv.org/abs/1912.06503

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