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Lévy walk approach to anomalous diffusion

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  • Klafter, J.
  • Blumen, A.
  • Zumofen, G.
  • Shlesinger, M.F.

Abstract

The transport properties of Lévy walks are discussed in the framework of continuous time random walks (CTRW) with coupled memories. This type of walks may lead to anomalous diffusion where the mean squared displacement 〈r2(t)〉∼tα with α≠1. We focus on the enhanced diffusion limit, α>1, in one dimension and present our results on 〈r2(t)〉, the mean number of distinct sites visited S(t) and P(r, t), the probability of being at position r at time t.

Suggested Citation

  • Klafter, J. & Blumen, A. & Zumofen, G. & Shlesinger, M.F., 1990. "Lévy walk approach to anomalous diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 168(1), pages 637-645.
    • Handle: RePEc:eee:phsmap:v:168:y:1990:i:1:p:637-645
    DOI: 10.1016/0378-4371(90)90416-P
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    References listed on IDEAS

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    1. Shlesinger, Michael F. & Klafter, Joseph & J. West, Bruce, 1986. "Levy walks with applications to turbulence and chaos," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 140(1), pages 212-218.
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    Cited by:

    1. Peng, Chung-Kang & Havlin, Shlomo & Schwartz, Moshe & Eugene Stanley, H. & Weiss, George H., 1991. "Algebraically decaying noise in a system of particles with hard-core interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 178(3), pages 401-405.
    2. Magdziarz, M. & Scheffler, H.P. & Straka, P. & Zebrowski, P., 2015. "Limit theorems and governing equations for Lévy walks," Stochastic Processes and their Applications, Elsevier, vol. 125(11), pages 4021-4038.
    3. Bernabó, P. & Burioni, R. & Lepri, S. & Vezzani, A., 2014. "Anomalous transmission and drifts in one-dimensional Lévy structures," Chaos, Solitons & Fractals, Elsevier, vol. 67(C), pages 11-19.
    4. Scalas, Enrico, 2006. "The application of continuous-time random walks in finance and economics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 362(2), pages 225-239.

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