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Generalised central limit theorems for growth rate distribution of complex systems

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  • Misako Takayasu
  • Hayafumi Watanabe
  • Hideki Takayasu

Abstract

We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling properties and distributions reported for growth rates of complex systems in a variety of fields can be derived from this basic physical model. Statistical data of growth rates for about 1 million business firms are analysed as a real-world example of randomly growing systems. Not only are the scaling relations consistent with the theoretical solution, but the entire functional form of the growth rate distribution is fitted with a theoretical distribution that has a power-law tail.

Suggested Citation

  • Misako Takayasu & Hayafumi Watanabe & Hideki Takayasu, 2013. "Generalised central limit theorems for growth rate distribution of complex systems," Papers 1301.2728, arXiv.org, revised Jan 2014.
  • Handle: RePEc:arx:papers:1301.2728
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    File URL: http://arxiv.org/pdf/1301.2728
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    References listed on IDEAS

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    1. Sergey V. Buldyrev & Jakub Growiec & Fabio Pammolli & Massimo Riccaboni & H. Eugene Stanley, 2007. "The Growth of Business Firms: Facts and Theory," Journal of the European Economic Association, MIT Press, vol. 5(2-3), pages 574-584, 04-05.
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    3. Massimo Riccaboni & Fabio Pammolli & Sergey V. Buldyrev & Linda Ponta & H. Eugene Stanley, 2009. "The Size Variance Relationship of Business Firm Growth Rates," ROCK Working Papers 052, Department of Computer and Management Sciences, University of Trento, Italy, revised 11 Jun 2009.
    4. De Fabritiis, G. & Pammolli, F. & Riccaboni, M., 2003. "On size and growth of business firms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 38-44.
    5. Dongfeng Fu & Fabio Pammolli & S. V. Buldyrev & Massimo Riccaboni & Kaushik Matia & Kazuko Yamasaki & H. E. Stanley, 2005. "The Growth of Business Firms: Theoretical Framework and Empirical Evidence," Papers physics/0512005, arXiv.org.
    6. Yamasaki, Kazuko & Matia, Kaushik & Buldyrev, Sergey V. & Fu, Dongfeng & Pammolli, Fabio & Riccaboni, Massimo & Stanley, H. Eugene, 2004. "Preferential attachment and growth dynamics in complex systems," MPRA Paper 15908, University Library of Munich, Germany, revised 06 Feb 2006.
    7. John Sutton, 1997. "Gibrat's Legacy," Journal of Economic Literature, American Economic Association, vol. 35(1), pages 40-59, March.
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    10. Bottazzi, Giulio & Dosi, Giovanni & Lippi, Marco & Pammolli, Fabio & Riccaboni, Massimo, 2001. "Innovation and corporate growth in the evolution of the drug industry," International Journal of Industrial Organization, Elsevier, vol. 19(7), pages 1161-1187, July.
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    Cited by:

    1. Thesmar , David & Landier , Augustin, 2014. "Instabilities in Large Economies: Aggregate Volatility Without Idiosyncratic Shocks," Les Cahiers de Recherche 1052, HEC Paris.

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