Large deviation principles are established for the two-parameter Poisson-Dirichlet distribution and two-parameter Dirichlet process when parameter $\theta$ approaches infinity. The motivation for these results is to understand the differences in terms of large deviations between the two-parameter models and their one-parameter counterparts. New insight is obtained about the role of the second parameter $\alpha$ through a comparison with the corresponding results for the one-parameter Poisson-Dirichlet distribution and Dirichlet process.
"Large Deviations for Dirichlet Processes and Poisson-Dirichlet Distribution with Two Parameters." Electron. J. Probab. 12 787 - 807, 2007. https://doi.org/10.1214/EJP.v12-417