Condensation Phenomena and Pareto Distribution in Disordered Urn Models

  • Jun-ichi Inoue
  • Jun Ohkubo
Part of the New Economic Windows book series (NEW)


We investigate equilibrium statistical properties of urn models with disorder. The model is introduced from the view point of the power-law behavior and randomness; it is clarified that quenched random parameters play an important role in generating power-law behavior.We evaluate the occupation probability P(k) with which an urn has k balls by using the concept of statistical physics of disordered systems. In the disordered urn model belonging to the Monkey class, we find that above critical density ρc for a given temperature, condensation phenomenon occurs and the occupation probability changes its scaling behavior from an exponentiallaw to a heavy tailed power-law in large k regime. We also discuss an interpretation of our results for explaining of macro-economy, in particular, emergence of wealth differentials.


Gini Index Pareto Distribution Wealth Distribution Occupation Probability Saddle Point Equation 
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© Springer-Verlag Italia 2010

Authors and Affiliations

  • Jun-ichi Inoue
    • 1
  • Jun Ohkubo
    • 2
  1. 1.Complex Systems Engineering, Graduate School of Information Science and TechnologyHokkaido University N14-W9SapporoJapan
  2. 2.Institute for Solid State PhysicsUniversity of TokyoChibaJapan

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