The Pitman-Yor, or Chinese restaurant process, is a stochastic process that generates distributions following a power law with exponents lower than 2, as found in 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.

Statistical mechanics of the “Chinese restaurant” process: lack of self-averaging, anomalous finite-size effects, and condensation / B. F. Bassetti, M. Zarei, M. Cosentino Lagomarsino, G. Bianconi. - In: PHYSICAL REVIEW E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS. - ISSN 1539-3755. - 80:6(2009), pp. 066118.066118.1-066118.066118.4.

Statistical mechanics of the “Chinese restaurant” process: lack of self-averaging, anomalous finite-size effects, and condensation

B. F. Bassetti
Primo
;
M. Cosentino Lagomarsino;
2009

Abstract

The Pitman-Yor, or Chinese restaurant process, is a stochastic process that generates distributions following a power law with exponents lower than 2, as found in 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.
Settore FIS/02 - Fisica Teorica, Modelli e Metodi Matematici
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/157088
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