title: 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 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.
authors.affiliation: Dipartimento di Fisica, Universitá degli Studi di Milano, via Celoria 16, Milano, Italy.
authors.forename: Bruno
authors.initials: B
authors.lastname: Bassetti
authors.forename: Mina
authors.initials: M
authors.lastname: Zarei
authors.forename: Marco
authors.initials: M
authors.lastname: Cosentino Lagomarsino
authors.forename: Ginestra
authors.initials: G
authors.lastname: Bianconi
mesh_terms: D000465:Algorithms; D001703:Biophysics / Q000379:methods*; D003198:Computer Simulation; D015233:Models, Statistical; D011336:Probability; D016008:Statistical Distributions; D013269:Stochastic Processes; D013314:Stress, Mechanical