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Some fundamental aspects of Lévy flights

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  • 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
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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).

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