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Phase transition in the rich-get-richer mechanism due to finite-size effects


  • James P. Bagrow
  • Jie Sun
  • Daniel ben-Avraham


The rich-get-richer mechanism (agents increase their ``wealth'' randomly at a rate proportional to their holdings) is often invoked to explain the Pareto power-law distribution observed in many physical situations, such as the degree distribution of growing scale free nets. We use two different analytical approaches, as well as numerical simulations, to study the case where the number of agents is fixed and finite (but large), and the rich-get-richer mechanism is invoked a fraction r of the time (the remainder of the time wealth is disbursed by a homogeneous process). At short times, we recover the Pareto law observed for an unbounded number of agents. In later times, the (moving) distribution can be scaled to reveal a phase transition with a Gaussian asymptotic form for r 1/2.

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  • James P. Bagrow & Jie Sun & Daniel ben-Avraham, 2007. "Phase transition in the rich-get-richer mechanism due to finite-size effects," Papers 0712.2220,, revised May 2008.
  • Handle: RePEc:arx:papers:0712.2220

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    References listed on IDEAS

    1. A. Chatterjee & B. K. Chakrabarti, 2007. "Kinetic exchange models for income and wealth distributions," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 60(2), pages 135-149, November.
    2. Arnab Chatterjee & Bikas K. Chakrabarti, 2007. "Kinetic Exchange Models for Income and Wealth Distributions," Papers 0709.1543,, revised Nov 2007.
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    Cited by:

    1. Behfar, Stefan Kambiz & Turkina, Ekaterina & Cohendet, Patrick & Burger-Helmchen, Thierry, 2016. "Directed networks’ different link formation mechanisms causing degree distribution distinction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 479-491.

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