Power-law behavior and condensation phenomena in disordered urn models

Details Power-law behavior and condensation phenomena in disordered urn models Power-law behavior and condensation phenomena in disordered urn models

2006-06-07

arxiv.org/abs/physics/0606068v4

Physics

Physics and Society

16pages, 9figures, using iopart.cls, 2 new figures were added

Scientific paper

We investigate equilibrium statistical properties of urn models with disorder. Two urn models are proposed; one belongs to the Ehrenfest class, and the other corresponds to the Monkey class. These models are 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 $\rho_\mathrm{c}$ for a given temperature, condensation phenomenon occurs and 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 interpretation of our results for explaining of macro-economy, in particular, emergence of wealth differentials.

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