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Almost sure central limit theorems in stochastic geometry

Part of: Limit theorems Stochastic processes

Published online by Cambridge University Press:  24 September 2020

Giovanni Luca Torrisi  and
Emilio Leonardi
Giovanni Luca Torrisi*
Affiliation:
Istituto per le Applicazioni del Calcolo, CNR
Emilio Leonardi*
Affiliation:
Politecnico di Torino
*
*Postal address: Via dei Taurini 19, 00185 Roma, Italy. Email: giovanniluca.torrisi@cnr.it
**Postal address: Corso Duca degli Abruzzi 24, 10129 Torino, Italy. Email: emilio.leonardi@polito.it
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Abstract

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.

Keywords

Almost sure limit theoremMalliavin calculusPoisson processrandom graphsstabilizationstochastic geometry

MSC classification

Primary: 60F05: Central limit and other weak theorems
Secondary: 60G55: Point processes
Type
Original Article
Information
Advances in Applied Probability , Volume 52 , Issue 3 , September 2020 , pp. 705 - 734
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Copyright
© Applied Probability Trust 2020

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