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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.

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  • 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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    References listed on IDEAS

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    Cited by:

    1. Thesmar , David & Landier , Augustin, 2014. "Instabilities in Large Economies: Aggregate Volatility Without Idiosyncratic Shocks," HEC Research Papers Series 1052, HEC Paris.
    2. Hayato Goto & Eduardo Viegas & Hideki Takayasu & Misako Takayasu & Henrik Jeldtoft Jensen, 2019. "Dynamics of essential interaction between firms on financial reports," PLOS ONE, Public Library of Science, vol. 14(12), pages 1-16, December.
    3. Hayato Goto & Hideki Takayasu & Misako Takayasu, 2017. "Estimating risk propagation between interacting firms on inter-firm complex network," PLOS ONE, Public Library of Science, vol. 12(10), pages 1-12, October.
    4. Sandro Claudio Lera & Didier Sornette, 2017. "Quantification of the evolution of firm size distributions due to mergers and acquisitions," PLOS ONE, Public Library of Science, vol. 12(8), pages 1-16, August.

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