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

James P. Bagrow, Jie Sun and Daniel ben-Avraham

Papers from arXiv.org

Abstract: 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.

Date: 2007-12, Revised 2008-05
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Citations: View citations in EconPapers (3)

Published in J. Phys. A: Math. Theor. 41 (2008) 185001

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