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The universal macroscopic statistics and phase transitions of rank distributions

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  • Eliazar, Iddo
  • Cohen, Morrel H.

Abstract

We establish a “Central Limit Theorem” for rank distributions, which provides a detailed characterization and classification of their universal macroscopic statistics and phase transitions. The limit theorem is based on the statistical notion of Lorenz curves, and is termed the “Lorenzian Limit Law” (LLL). Applications of the LLL further establish: (i) a statistical explanation for the universal emergence of Pareto’s law in the context of rank distributions; (ii) a statistical classification of universal macroscopic network topologies; (iii) a statistical classification of universal macroscopic socioeconomic states; (iv) a statistical classification of Zipf’s law, and a characterization of the “self-organized criticality” it manifests.

Suggested Citation

  • Eliazar, Iddo & Cohen, Morrel H., 2011. "The universal macroscopic statistics and phase transitions of rank distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4293-4303.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:23:p:4293-4303
    DOI: 10.1016/j.physa.2011.06.049
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    References listed on IDEAS

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    1. Bouchaud,Jean-Philippe & Potters,Marc, 2009. "Theory of Financial Risk and Derivative Pricing," Cambridge Books, Cambridge University Press, number 9780521741866.
    2. Mantegna,Rosario N. & Stanley,H. Eugene, 2007. "Introduction to Econophysics," Cambridge Books, Cambridge University Press, number 9780521039871.
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    Cited by:

    1. Luckstead, Jeff & Devadoss, Stephen & Danforth, Diana, 2017. "The size distributions of all Indian cities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 474(C), pages 237-249.

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