  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.

Physics and Society;Data Analysis, Statistics and Probability