  The Pitman-Yor, or Chinese Restaurant Process, is a stochastic process that
generates distributions following a power-law with exponents lower than two, as
found in a numerous physical, biological, technological and social systems. We
discuss its rich behavior with the tools and viewpoint of statistical
mechanics. We show that this process invariably gives rise to a condensation,
i.e. a distribution dominated by a finite number of classes. We also evaluate
thoroughly the finite-size effects, finding that the lack of stationary state
and self-averaging of the process creates realization-dependent cutoffs and
behavior of the distributions with no equivalent in other statistical
mechanical models.
