Almost sure central limit theorems in stochastic geometry

We prove an almost sure central limit theorem on the Poisson space, which is perfectly tailored for stabilizing functionals arising 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...

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Bibliographic Details
Published inAdvances in applied probability Vol. 52; no. 3; pp. 705 - 734
Main Authors Torrisi, Giovanni Luca, Leonardi, Emilio
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.09.2020
Applied Probability Trust
Subjects
Approximation
Geometry
Original Article
Original Articles
Probability
Random variables
Tessellation
Theorems
60G55
stabilization
random graphs
Malliavin calculus
stochastic geometry
Poisson process
Almost sure limit theorem
60F05
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Summary:We prove an almost sure central limit theorem on the Poisson space, which is perfectly tailored for stabilizing functionals arising 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, and (iii) the volume of the set approximation via the Poisson–Voronoi tessellation.
ISSN:0001-8678
1475-6064
DOI:10.1017/apr.2020.15