The Poisson-Dirichlet Distribution and Related Topics: Models and Asymptotic Behaviors (Probability and Its Applications)

Preface
Contents
Part I Models
	Introduction
		Discrete Models
			Genetic Background
			The Wright--Fisher Model
			The Moran Model
		Diffusion Approximation
		An Important Relation
		Notes
	The Poisson--Dirichlet Distribution
		Definition and Poisson Process Representation
		Perman\'s Formula
		Marginal Distribution
		Size-biased Sampling and the GEM Representation
		The Ewens Sampling Formula
		Scale-invariant Poisson Process
		Urn-based Models
			Hoppe\'s Urn
			Linear Birth Process with Immigration
			A Model of Joyce and Tavaré
		The Dirichlet Process
		Notes
	The Two-Parameter Poisson--Dirichlet Distribution
		Definition
		Marginal Distributions
		The Pitman Sampling Formula
		Urn-type Construction
		Notes
	The Coalescent
		Kingman\'s n-Coalescent
		The Coalescent
		The Pure-death Markov Chain
		Notes
	Stochastic Dynamics
		Infinitely-many-neutral-alleles Model
		A Fleming--Viot Process
		The Structure of Transition Functions
		A Measure-valued Branching Diffusion with Immigration
		Two-parameter Generalizations
		Notes
	Particle Representation
		Exchangeability and Random Probability Measures
		The Moran Process and the Fleming--Viot Process
		The Donnelly--Kurtz Look-down Process
		Embedded Coalescent
		Notes
Part II Asymptotic Behaviors
	Fluctuation Theorems
		The Poisson--Dirichlet Distribution
		The Dirichlet Process
		Gaussian Limits
		Notes
	Large Deviations for the Poisson--Dirichlet Distribution
		Large Mutation Rate
			The Poisson--Dirichlet Distribution
			The Two-parameter Poisson--Dirichlet Distribution
		Small Mutation Rate
			The Poisson--Dirichlet Distribution
			Two-parameter Generalization
		Applications
		Notes
	Large Deviations for the Dirichlet Processes
		One-parameter Case
		Two-parameter Case
		Comparison of Rate Functions
		Notes
Poisson Process and Poisson Random Measure
	Definitions
	Properties
Basics of Large Deviations
References
Index