The Poisson-Dirichlet Distribution and Related Topics: Models and Asymptotic Behaviors

Preface.- Part I: Models.- 1. Introduction.- 2. The Poisson–Dirichlet Distribution.- 3. The Two-Parameter Poisson–Dirichlet Distribution.- 4. The Coalescent.- 5. Stochastic Dynamics.- 6. Particle Representation.- Part II: Asymptotic Behaviors.- 7. Fluctuation Theorems.- 8. Large Deviations for the Poisson–Dirichlet Distribution.- 9. Large Deviations for the Dirichlet Processes.- A. Poisson Process and Poisson Random Measure.- A.1. Definitions.- A.2. Properties.- B. Basics of Large Deviations.- References.- Index.