Multivariate central limit theorems for random simplicial complexes

Autor(en): Akinwande, Grace
Reitzner, Matthias 
Stichwörter: Central limit theorem; FINE GAUSSIAN FLUCTUATIONS; Mathematics; Mathematics, Applied; NORMAL APPROXIMATION; Poisson point process; POISSON SPACE; Random simplicial complex; TOPOLOGY
Erscheinungsdatum: 2020
Herausgeber: ACADEMIC PRESS INC ELSEVIER SCIENCE
Journal: ADVANCES IN APPLIED MATHEMATICS
Volumen: 121
Zusammenfassung: 
Consider a Poisson point process within a convex set in a Euclidean space. The Vietoris-Rips complex is the clique complex over the graph connecting all pairs of points with distance at most delta. Summing powers of the volume of all k-dimensional faces defines the volume-power functionals of these random simplicial complexes. The asymptotic behavior of the volume-power functionals of the Vietoris-Rips complex is investigated as the intensity of the underlying Poisson point process tends to infinity and the distance parameter goes to zero. Univariate and multivariate central limit theorems are proven. Analogous results for the Cech complex are given. (C) 2020 Elsevier Inc. All rights reserved.
ISSN: 01968858
DOI: 10.1016/j.aam.2020.102076

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