Preprint

Almost sure central limit theorems in stochastic geometry

Giovanni-Luca TorrisiIstituto per le Applicazioni del Calcolo, CNREmilio LeonardiPolitecnico di Torino

Advances in Applied Probabilityjournal2020en

ABI

Abstract

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.

Topics

Geometry and complex manifolds Geometric Analysis and Curvature Flows Point processes and geometric inequalities

Identifiers

DOI: 10.1017/apr.2020.15

Citations and references

Cited by 025 references

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