Thermodynamic limits of macroeconomic or financial models: One- and two-parameter Poisson-Dirichlet models

Their behavior as the model sizes tend to infinity (thermodynamic limits) are qualitatively very different. In the one-parameter models, the number of clusters and components of partition vectors are both self-averaging, that is, their coefficients of variations tend to zero as the model sizes become very large, while in the two-parameter models they are not self-averaging, namely, their coefficients of variations do not tend to zero as model sizes becomes large.