On limit theorems for persistent Betti numbers from dependent data

• Verfasst von: Krebs, Johannes [VerfasserIn]
• Titel: On limit theorems for persistent Betti numbers from dependent data
• Verf.angabe: Johannes Krebs
• E-Jahr: 2021
• Jahr: 7 May 2021
• Umfang: 36 S.
• Fussnoten: Gesehen am 09.09.2021
• Titel Quelle: Enthalten in: Stochastic processes and their applications
• Ort Quelle: Amsterdam [u.a.] : Elsevier, 1973
• Jahr Quelle: 2021
• Band/Heft Quelle: 139(2021) vom: Sept., Seite 139-174
• ISSN Quelle: 1879-209X
• DOI: doi:10.1016/j.spa.2021.04.013
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Critical regime
• Sach-SW: Dependent data
• Sach-SW: Limit theorems
• Sach-SW: Markov chains
• Sach-SW: Marton coupling
• Sach-SW: Topological data analysis
• K10plus-PPN: 1769953574

Abstract

We study persistent Betti numbers and persistence diagrams obtained from time series and random fields. It is well known that the persistent Betti function is an efficient descriptor of the topology of a point cloud. So far, convergence results for the (r,s)-persistent Betti number of the qth homology group, βqr,s, were mainly considered for finite-dimensional point cloud data obtained from i.i.d. observations or stationary point processes such as a Poisson process. In this article, we extend these considerations. We derive limit theorems for the pointwise convergence of persistent Betti numbers βqr,s in the critical regime under quite general dependence settings.