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Log-periodic oscillations for biased diffusion on random lattice

Author

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  • Stauffer, Dietrich
  • Sornette, Didier

Abstract

Random walks with a fixed bias direction on randomly diluted cubic lattices far above the percolation threshold exhibit log-periodic oscillations in the effective exponent versus time. A scaling argument accounts for the numerical results in the limit of large biases and small dilution and shows the importance of the interplay of these two ingredients in the generation of the log-periodicity. These results show that log-periodicity is the dominant effect compared to previous predictions of and reports on anomalous diffusion.

Suggested Citation

  • Stauffer, Dietrich & Sornette, Didier, 1998. "Log-periodic oscillations for biased diffusion on random lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 252(3), pages 271-277.
    • Handle: RePEc:eee:phsmap:v:252:y:1998:i:3:p:271-277
    DOI: 10.1016/S0378-4371(97)00680-8
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    Cited by:

    1. Nigmatullin, Raoul R. & Toboev, Vyacheslav A. & Lino, Paolo & Maione, Guido, 2015. "Reduced fractal model for quantitative analysis of averaged micromotions in mesoscale: Characterization of blow-like signals," Chaos, Solitons & Fractals, Elsevier, vol. 76(C), pages 166-181.
    2. Sornette, Didier & Johansen, Anders, 1998. "A hierarchical model of financial crashes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 261(3), pages 581-598.
    3. George Chang & James Feigenbaum, 2006. "A Bayesian analysis of log-periodic precursors to financial crashes," Quantitative Finance, Taylor & Francis Journals, vol. 6(1), pages 15-36.
    4. Makowiec, D. & Gnaciński, P. & Miklaszewski, W., 2004. "Amplified imitation in percolation model of stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 331(1), pages 269-278.

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