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Theory of Zipf's Law and of General Power Law Distributions with Gibrat's law of Proportional Growth

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  • A. Saichev
  • Y. Malevergne
  • D. Sornette

Abstract

We summarize a book under publication with his title written by the three present authors, on the theory of Zipf's law, and more generally of power laws, driven by the mechanism of proportional growth. The preprint is available upon request from the authors. For clarity, consistence of language and conciseness, we discuss the origin and conditions of the validity of Zipf's law using the terminology of firms' asset values. We use firms at the entities whose size distributions are to be explained. It should be noted, however, that most of the relations discussed in this book, especially the intimate connection between Zipf's and Gilbrat's laws, underlie Zipf's law in diverse scientific areas. The same models and variations thereof can be straightforwardly applied to any of the other domains of application.

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File URL: http://arxiv.org/pdf/0808.1828
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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 0808.1828.

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Date of creation: Aug 2008
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Publication status: Published in Theory of Zipf's Law and beyond, Lecture Notes in Economics and Mathematical Systems, Volume 632, Springer (November 2009) ISBN: 978-3-642-02945-5
Handle: RePEc:arx:papers:0808.1828

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  1. Fujiwara, Yoshi & Di Guilmi, Corrado & Aoyama, Hideaki & Gallegati, Mauro & Souma, Wataru, 2004. "Do Pareto–Zipf and Gibrat laws hold true? An analysis with European firms," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 335(1), pages 197-216.
  2. Gaffeo, Edoardo & Gallegati, Mauro & Palestrini, Antonio, 2003. "On the size distribution of firms: additional evidence from the G7 countries," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 324(1), pages 117-123.
  3. Xavier Gabaix, 1999. "Zipf'S Law For Cities: An Explanation," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 114(3), pages 739-767, August.
  4. Fujiwara, Yoshi & Aoyama, Hideaki & Di Guilmi, Corrado & Souma, Wataru & Gallegati, Mauro, 2004. "Gibrat and Pareto–Zipf revisited with European firms," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 344(1), pages 112-116.
  5. Xavier Gabaix & Yannis M. Ioannides, 2003. "The Evolution of City Size Distributions," Discussion Papers Series, Department of Economics, Tufts University, Department of Economics, Tufts University 0310, Department of Economics, Tufts University.
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