Power-law behavior and condensation phenomena in disordered urn models

We investigate equilibrium statistical properties of a disordered urn model. New types of urn models are proposed, in which quenched disorder 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 our new disordered urn model, we find that above critical density ρc for a given temperature, condensation phenomenon occurs and most of the balls are condensed into an urn with the lowest energy level. As the result, the occupation probability changes its scaling behavior from an exponential-law to a heavy tailed power-law in large k regime. We also discuss an application of our results for explaining of macro economy, in particular, emergence of wealth differentials. PACS numbers: 02.50.-r, 05.20.-y, 05.30.Jp Submitted to: J. Phys. A: Math. Gen. Power-law behavior and condensation phenomena in disordered urn models 2