Journal article
Convergence of persistence diagrams for discrete time stationary processes: Convergence of persistence diagrams
Journal of applied and computational topology, Vol.9(2), 14
06/2025
DOI: 10.1007/s41468-025-00211-1
Appears in UI Libraries Support Open Access
Abstract
In this article we establish two fundamental results for the sublevel set persistent homology for stationary processes indexed by the positive integers. The first is a strong law of large numbers for the persistence diagram (treated as a measure “above the diagonal” in the extended plane) evaluated on a large class of sets and functions, beyond continuous functions with compact support. We prove this result subject to only minor conditions that the sequence is ergodic and the tails of the marginals are not too heavy. The second result is a central limit theorem for the persistence diagram evaluated on the class of all step functions; this result holds as long as a -mixing criterion is satisfied and the distributions of the partial maxima do not decay too slowly. Our results greatly expand those extant in the literature to allow for more fruitful use in statistical applications, beyond idealized settings. Examples of distributions and functions for which the limit theory holds are provided throughout.
Details
- Title: Subtitle
- Convergence of persistence diagrams for discrete time stationary processes: Convergence of persistence diagrams
- Creators
- Andrew M. Thomas - Department of Statistics and Actuarial Science, University of Iowa
- Resource Type
- Journal article
- Publication Details
- Journal of applied and computational topology, Vol.9(2), 14
- DOI
- 10.1007/s41468-025-00211-1
- ISSN
- 2367-1726
- eISSN
- 2367-1734
- Publisher
- Springer Nature
- Grant note
- 1940124 / Office of Advanced Cyberinfrastructure (http://dx.doi.org/10.13039/100000105) 2114143 / Division of Mathematical Sciences (http://dx.doi.org/10.13039/100000121)
- Language
- English
- Date published
- 06/2025
- Academic Unit
- Statistics and Actuarial Science
- Record Identifier
- 9984825530702771
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