IDEAS home Printed from https://ideas.repec.org/a/bla/scjsta/v49y2022i1p427-454.html
   My bibliography  Save this article

Functional central limit theorems for persistent Betti numbers on cylindrical networks

Author

Listed:
  • Johannes Krebs
  • Christian Hirsch

Abstract

We study functional central limit theorems for persistent Betti numbers obtained from networks defined on a Poisson point process. The limit is formed in large volumes of cylindrical shape stretching only in one dimension. The results cover a directed sublevel‐filtration for stabilizing networks and the Čech and Vietoris–Rips complex on the random geometric graph. The presented functional central limit theorems open the door to a variety of statistical applications in topological data analysis and we consider goodness‐of‐fit tests in a simulation study.

Suggested Citation

  • Johannes Krebs & Christian Hirsch, 2022. "Functional central limit theorems for persistent Betti numbers on cylindrical networks," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(1), pages 427-454, March.
    • Handle: RePEc:bla:scjsta:v:49:y:2022:i:1:p:427-454
    DOI: 10.1111/sjos.12524
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/sjos.12524
    Download Restriction: no
    File URL: https://libkey.io/10.1111/sjos.12524?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. M. Saadatfar & H. Takeuchi & V. Robins & N. Francois & Y. Hiraoka, 2017. "Pore configuration landscape of granular crystallization," Nature Communications, Nature, vol. 8(1), pages 1-11, August.
    2. Youri Davydov & Ričardas Zitikis, 2008. "On weak convergence of random fields," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(2), pages 345-365, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Bonnet, Gilles & Hirsch, Christian & Rosen, Daniel & Willhalm, Daniel, 2023. "Limit theory of sparse random geometric graphs in high dimensions," Stochastic Processes and their Applications, Elsevier, vol. 163(C), pages 203-236.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Davydov, Youri & Tempelman, Arkady, 2024. "Randomized limit theorems for stationary ergodic random processes and fields," Stochastic Processes and their Applications, Elsevier, vol. 174(C).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:scjsta:v:49:y:2022:i:1:p:427-454. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0303-6898 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.