Poisson and Gaussian fluctuations for the components of the f-vector of high-dimensional random simplicial complexes

Autor(en): Grygierek, Jens
Stichwörter: central limit theorem; high dimensional random Vietoris-Rips complex; Mathematics; phase transition; Poisson limit theorem; Poisson point process; second-order Poincare inequality; Statistics & Probability; stochastic geometry
Erscheinungsdatum: 2020
Herausgeber: IMPA
Journal: ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS
Volumen: 17
Ausgabe: 2
Startseite: 675
Seitenende: 709
Zusammenfassung: 
We investigate the high-dimensional asymptotic distributional behavior of the components of the f-vector of a random Vietoris-Rips complex that is generated over a Poisson point process in [-1/2, 1/2](d) as the space dimension and the intensity tend to infinity while the radius parameter tends to zero simultaneously.
ISSN: 19800436
DOI: 10.30757/ALEA.v17-26

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