Condensation Phenomena and Pareto Distribution in Disordered Urn Models

Abstract

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.