You are here

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

TitleStatistical mechanics of the "Chinese restaurant process": lack of self-averaging, anomalous finite-size effects, and condensation.
Publication TypeJournal Article
Year of Publication2009
AuthorsBassetti, B, Zarei, M, Cosentino Lagomarsino, M, Bianconi, G
JournalPhys Rev E Stat Nonlin Soft Matter Phys
Volume80
Issue6 Pt 2
Pagination066118
Date Published2009 Dec
ISSN1550-2376
KeywordsAlgorithms, Biophysics, Computer Simulation, Models, Statistical, Probability, Statistical Distributions, Stochastic Processes, Stress, Mechanical
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.

Alternate JournalPhys Rev E Stat Nonlin Soft Matter Phys
PubMed ID20365242