A FINITARY CHARACTERIZATION OF THE EWENS SAMPLING FORMULA

U. Garibaldi (), D. Costantini and P. Viarengo ()
Additional contact information
U. Garibaldi: IMEM-CNR, c/o Department of Physics, University of Genoa, via Dodecaneso 33, Genoa, 16123, Italy
D. Costantini: National Cancer Research Institute (IST), Largo Benzi 10, Genoa, 16132, Italy;
P. Viarengo: National Cancer Research Institute (IST), Largo Benzi 10, Genoa, 16132, Italy;

Advances in Complex Systems (ACS), 2004, vol. 07, issue 02, 265-284

Abstract: The clustering of agents in the market is a typical problem dealt with in recent approaches to macroeconomic modeling, describing macroscopic variables in terms of the behavior of a large collection of microeconomic entities. Clustering is subject to many economic interpretations, often described by the Ewens Sampling Formula (ESF). In contrast with the usual complex derivations, we suggest a finitary characterization of the ESF pointing to real economic processes. Our approach is finitary in the sense that we provide a probabilistic description of a system ofnindividuals considered as a closed system, a population, where individuals can change attributes over time. The probability is understood as the fraction of time the system spends in the considered partition. As the ESF represents an equilibrium distribution satisfying detailed balance, some properties difficult to prove are derived in a simple way. Besides the mean distribution of the cluster sizes, we study the probabilistic time behavior of clusters, in particular the mean survival as a function of the actual size and the correlation between size and age.

Keywords: Ewens sampling formula; herd behavior; Ehrenfest–Brillouin model; probabilistic dynamics (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (1)

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DOI: 10.1142/S0219525904000172

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