IDEAS home Printed from https://ideas.repec.org/a/spr/eurphb/v79y2011i1p115-120.html
   My bibliography  Save this article

Fractal Weyl law for Linux Kernel architecture

Author

Listed:
  • L. Ermann
  • A. D. Chepelianskii
  • D. L. Shepelyansky

Abstract

We study the properties of spectrum and eigenstates of the Google matrix of a directed network formed by the procedure calls in the Linux Kernel. Our results obtained for various versions of the Linux Kernel show that the spectrum is characterized by the fractal Weyl law established recently for systems of quantum chaotic scattering and the Perron-Frobenius operators of dynamical maps. The fractal Weyl exponent is found to be ν ≈ 0.65 that corresponds to the fractal dimension of the network d ≈ 1.3. An independent computation of the fractal dimension by the cluster growing method, generalized for directed networks, gives a close value d ≈ 1.4. The eigenmodes of the Google matrix of Linux Kernel are localized on certain principal nodes. We argue that the fractal Weyl law should be generic for directed networks with the fractal dimension d > 2. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2011

Suggested Citation

  • L. Ermann & A. D. Chepelianskii & D. L. Shepelyansky, 2011. "Fractal Weyl law for Linux Kernel architecture," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 79(1), pages 115-120, January.
  • Handle: RePEc:spr:eurphb:v:79:y:2011:i:1:p:115-120
    DOI: 10.1140/epjb/e2010-10774-7
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1140/epjb/e2010-10774-7
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1140/epjb/e2010-10774-7?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.

    Citations

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


    Cited by:

    1. Célestin Coquidé & José Lages & Leonardo Ermann & Dima Shepelyansky, 2022. "COVID-19 impact on the international trade," Post-Print hal-03536528, HAL.

    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:spr:eurphb:v:79:y:2011:i:1:p:115-120. 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.