IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v34y2007i1p129-142.html
   My bibliography  Save this article

Some fundamental aspects of Lévy flights

Author

Listed:
  • Metzler, Ralf
  • Chechkin, Aleksei V.
  • Gonchar, Vsevolod Yu.
  • Klafter, Joseph

Abstract

We investigate the physical basis and properties of Lévy flights (LFs), Markovian random walks with a long-tailed density of jump lengths, λ(ξ)∼|ξ|-1-α, with 0<α<2. In particular, we show that non-trivial boundary conditions need to be carefully posed, and that the method of images fails due to the non-locality of LFs. We discuss the behaviour of LFs in external potentials, demonstrating the existence of multimodal solutions whose maxima do not coincide with the potential minimum. The Kramers escape of LFs is investigated, and the physical nature of the a priori diverging kinetic energy of an LF is addressed.

Suggested Citation

  • Metzler, Ralf & Chechkin, Aleksei V. & Gonchar, Vsevolod Yu. & Klafter, Joseph, 2007. "Some fundamental aspects of Lévy flights," Chaos, Solitons & Fractals, Elsevier, vol. 34(1), pages 129-142.
    • Handle: RePEc:eee:chsofr:v:34:y:2007:i:1:p:129-142
    DOI: 10.1016/j.chaos.2007.01.055
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077907000951
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2007.01.055?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. Hirsch, Christian & Jahnel, Benedikt & Cali, Elie, 2022. "Percolation and connection times in multi-scale dynamic networks," Stochastic Processes and their Applications, Elsevier, vol. 151(C), pages 490-518.
    2. Zeng, Lingzao & Li, Jianlong & Shi, Jiachun, 2012. "M-ary signal detection via a bistable system in the presence of Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 45(4), pages 378-382.
    3. Tawfik, Ashraf M. & Elkamash, I.S., 2022. "On the correlation between Kappa and Lévy stable distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 601(C).
    4. Joelson, Maminirina & Golder, Jacques & Beltrame, Philippe & Néel, Marie-Christine & Di Pietro, Liliana, 2016. "On fractal nature of groundwater level fluctuations due to rainfall process," Chaos, Solitons & Fractals, Elsevier, vol. 82(C), pages 103-115.

    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:eee:chsofr:v:34:y:2007:i:1:p:129-142. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.