Abstract
Several aspects of anomalous diffusion and their relationship to Lévy flights and walks are reviewed. We summarize the basic ideas of the Lévy-walk approach and discuss the ballistic-localized motion dichotomy, stationarity, escape times in conservative systems, and symbolic dynamics.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Bardou, F., Bouchaud, J.P., Emile, O., Aspect, A., Cohen-Tannodji, C. (1994): Phys. Rev. Lett. 72, 203
Barkai, E., Klafter, J. (1998): in “Chaos, Kinetics, and Nonlinear Dynamics in Fluids and Plasmas”, G.M. Zaslavsky and S. Benkadda eds. (Springer, Berlin) in press
Benkadda, S., Kassibrakis, S., White, R.B., Zaslavsky, G.M. (1997): Phys. Rev. E55, 4909
Bouchaud, J.-P. Georges, A. (1990): Phys. Rep. 195, 127
Chirikov, B.V., Shepelyansky, D.L. (1984): Physica D 13, 394
Chirikov, B.V., Shepelyansky, D.L. (1988): in “Renormalization Group”, World Scientific
Chirikov, B.V., Shepelyansky, D.L. (1988): Phys. Rev. Lett. 61, 1039
Feller, W. (1971): “An Introduction to Probability Theory and its Applications” (Wiley, New York)
Geisel, T., Zacherl, A., Radons, G. (1988): Z. Phys. B71, 117
Hao Bai-lin, (1989): Elementary Symbolic Dynamics and Chaos in Dissipative Systems (World Scientific, Singapore)
Ishizaki, R., Hata, H., Horita, T., Mori, H. (1990a): Prog. Theor. Phys. 84, 179
Ishizaki, R., Horita, T., Kobayashi, T., Mori, H. (1991): Prog. Theor. Phys. 85, 1013
Ishizaki, R., Hata, H., Horita, T., Mori, H. (1990b): Prog. Theor. Phys. 84, 179
Ishizaki, R., Mori, H. (1997): Prog. Theor. Phys. 97, 201
Karney, C.F.F. (1993): Physica D 8, 360
Klafter, J., Zumofen, G. (1993): Physica A196, 102
Klafter, J., Zumofen, G. (1994): Phys. Rev. E49, 4873
Klafter, J., Shlesinger, M.F., Zumofen, G. (1996): Physics Today, 49, No. 2, 33
Lévy, P. (1937): “Théorie de l'addition des variables aléatoires”, Gauthier Villars, Paris)
Mandelbrot, B. (1982): “The Fractal Geometry in Nature” (Freeman, San Francisco)
Meiss, J.D. (1997): Chaos, 7, 139
Ott, A., Bouchaud, J.P., Langevin, D., Urbach, W. (1990): Phys. Rev. Lett. 65, 2201
Schreckenberg, M. (1985): Z. Phys. B 60, 483
Shlesinger, M.F., Klafter, J. (1985): Phys. Rev. Lett. 54, 2551
Shlesinger, M.F., West, B.J., Klafter, J. (1987): Phys. Rev. Lett. 58, 1100
Shlesinger, M.F., Zaslavsky, G.M., Klafter, J. (1993): Nature 263, 31
Solomon, T.H., Weeks, E.R., Swinney, H.L. (1993): Phys. Rev. Lett. 71, 3975
Tabeling, P., Hansen, A.E., Paret, J. (1998): in “Chaos, Kinetics, and Nonlinear Dynamics in Fluids and Plasmas”, G.M. Zaslavsky and S. Benkadda eds. (Springer, Berlin) in press
Trefán, G., Floriani, E., West, B.J., Grigolini, P. (1994): Phys. Rev. E 50, 2564
Viswanathan, G.M., Afansyev, V., Buldyrev, S.V., Murphy, E.J., Prince, P.A., Stanley, H.E. (1996): Nature 381, 413
Zaslavsky, G.M., Stevens, D., Weitzner, H. (1993): Phys. Rev. E48, 1683
Zumofen, G., Klafter, J., Blumen, A. (1991): Phys. Rev. A, 44, 8390
Zumofen, G., Klafter, J. (1993a): Phys. Rev. E47, 851
Zumofen, G., Klafter, J., Blumen, A. (1993b): Phys. Rev. E 47, 2183
Zumofen, G., Klafter, J. (1994a): Chem. Phys. Lett. 219, 303
Zumofen, G., Klafter, J. (1994b): Z. Naturforsch. 49a, 1141
Zumofen, G., Klafter, J. (1994c): Europhys. Lett. 25, 565
Zumofen, G., Klafter, J. (1995): Phys. Rev. E, 51, 1818
Zumofen, G., Klafter, J.: to be published.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1999 Springer-Verlag
About this paper
Cite this paper
Zumofen, G., Klafter, J., Shlesinger, M.F. (1999). Lévy flights and Lévy walks revisited. In: Pękalski, A., Sznajd-Weron, K. (eds) Anomalous Diffusion From Basics to Applications. Lecture Notes in Physics, vol 519. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0106830
Download citation
DOI: https://doi.org/10.1007/BFb0106830
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-65416-2
Online ISBN: 978-3-540-49259-7
eBook Packages: Springer Book Archive