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Mechanisms for Power Laws

  • Didier Sornette
Part of the Springer Series in Synergetics book series (SSSYN)

Abstract

Power law distributions are ubiquitous statistical features of natural systems and are found in many different scientific disciplines. Indeed, many natural phenomena have power law size distributions reading, in the notation of Chap. 4,
$$P(x) \propto \frac{1}{{{x^1} + \mu }}$$
(14.1)
up to some large limiting cut-off [463, 7, 607]. In expression (14.1), P(x)dx is the probability to observe the variable in the range between x and x + dx. Power laws seem to also describe a large ensemble of social and economic statistics [553, 828, 461, 233, 792, 469, 470, 29].

Keywords

Acoustic Emission Ising Model Multiplicative Noise Hysteretic Loop Random Field Ising Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Didier Sornette
    • 1
    • 2
  1. 1.Institute of Geophysics and Planetary Physics and Department of Earth and Space Sciences, 3845 Slichter HallUniversity of CaliforniaLos AngelesUSA
  2. 2.Laboratoire de Physique de la Matière Condensée, CNRS UMR6622, Faculté des SciencesUniversité des SciencesNice Cedex 2France

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