Large deviations associated with Poisson–Dirichlet distribution and Ewens sampling formula

Several results of large deviations are obtained for distributions that are associated with the Poisson–Dirichlet distribution and the Ewens sampling formula when the parameter θ approaches infinity. The motivation for these results comes from a desire of understanding the exact meaning of θ going to infinity. In terms of the law of large numbers and the central limit theorem, the limiting procedure of θ going to infinity in a Poisson–Dirichlet …