Statistical Mechanics of the Chinese Restaurant Process: lack of self-averaging, anomalous finite-size effects and condensation

Abstract

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.

(5pages, 1 figure)

References in corpus (4)

• Critical phenomena in complex networks
• Scale-free networks with an exponent less than two
• Dynamics of the condensate in zero-range processes
• Stationary and dynamical properties of a zero range process on scale-free networks

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