Almost Sure Central Limit Theorems in Stochastic Geometry

2019/12/13 by Torrisi, Giovanni-Luca, Leonardi, Emilio
#60D05 #60F05 #60G55 #60H07 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1912.06503

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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