This paper examines asymptotic behavior of two types of economic or ?nancial models with manyinteracting heterogeneous agents. They are one-parameter Poisson-Dirichlet models, also called Ewens models, and its extension totwo-parameterPoisson-Dirichlet models. The total number of clusters, and the components of partition vectors (thenumberof clustersofspeci?ed sizes),both suitably normalizedby some powers of model sizes, of these classes of models are shown tobe related to the Mittag-Le?er distributions. Theirbehavior as the model sizes tend to in?nity(thermodynamic limits) are qualitativelyvery di?erent.Inthe one-parametermodels,thenumberof clusters, and components of partition vectors are both self-averaging, that is,theircoe?cientsofvariationstendto zeroasthemodelsizesbecomevery large, while in the two-parameter models they are not self-averaging, that is,theircoe?cientsofvariationsdonottendto zeroasmodel sizesbecomes large.
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Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number
CIRJE-F-445.
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