Multivariate central limit theorems for random simplicial complexes

DC FieldValueLanguage
dc.contributor.authorAkinwande, Grace
dc.contributor.authorReitzner, Matthias
dc.date.accessioned2021-12-23T15:57:51Z-
dc.date.available2021-12-23T15:57:51Z-
dc.date.issued2020
dc.identifier.issn01968858
dc.identifier.urihttps://osnascholar.ub.uni-osnabrueck.de/handle/unios/3179-
dc.description.abstractConsider 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.
dc.description.sponsorshipGerman Research AssociationGerman Research Foundation (DFG) [DFG-GRK 1916]; Supported by the German Research AssociationDFG-GRK 1916.
dc.language.isoen
dc.publisherACADEMIC PRESS INC ELSEVIER SCIENCE
dc.relation.ispartofADVANCES IN APPLIED MATHEMATICS
dc.subjectCentral limit theorem
dc.subjectFINE GAUSSIAN FLUCTUATIONS
dc.subjectMathematics
dc.subjectMathematics, Applied
dc.subjectNORMAL APPROXIMATION
dc.subjectPoisson point process
dc.subjectPOISSON SPACE
dc.subjectRandom simplicial complex
dc.subjectTOPOLOGY
dc.titleMultivariate central limit theorems for random simplicial complexes
dc.typejournal article
dc.identifier.doi10.1016/j.aam.2020.102076
dc.identifier.isiISI:000577542300001
dc.description.volume121
dc.identifier.eissn10902074
dc.publisher.place525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA
dcterms.isPartOf.abbreviationAdv. Appl. Math.
dcterms.oaStatusGreen Submitted
crisitem.author.deptFB 06 - Mathematik/Informatik-
crisitem.author.deptidfb06-
crisitem.author.parentorgUniversität Osnabrück-
crisitem.author.netidReMa759-
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