IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v38y2025i2d10.1007_s10959-025-01411-2.html
   My bibliography  Save this article

Zero–One Laws for Events with Positional Symmetries

Author

Listed:
  • Yahya Ayach

    (American University of Beirut)

  • Anthony Khairallah

    (American University of Beirut)

  • Tia Manoukian

    (American University of Beirut)

  • Jad Mchaimech

    (American University of Beirut)

  • Adam Salha

    (American University of Beirut)

  • Siamak Taati

    (American University of Beirut
    American University of Beirut)

Abstract

We use an information-theoretic argument due to O’Connell (2000) to prove that every sufficiently symmetric event concerning a countably infinite family of independent and identically distributed random variables is deterministic (i.e., has a probability of either 0 or 1). The i.i.d. condition can be relaxed. This result encompasses the Hewitt–Savage zero–one law and the ergodicity of the Bernoulli process, but also applies to other scenarios such as infinite random graphs and simple renormalization processes.

Suggested Citation

  • Yahya Ayach & Anthony Khairallah & Tia Manoukian & Jad Mchaimech & Adam Salha & Siamak Taati, 2025. "Zero–One Laws for Events with Positional Symmetries," Journal of Theoretical Probability, Springer, vol. 38(2), pages 1-20, June.
    • Handle: RePEc:spr:jotpro:v:38:y:2025:i:2:d:10.1007_s10959-025-01411-2
    DOI: 10.1007/s10959-025-01411-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-025-01411-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10959-025-01411-2?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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:spr:jotpro:v:38:y:2025:i:2:d:10.1007_s10959-025-01411-2. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.