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Mathematics - Probability Theory and Stochastic Processes | The Poisson-Dirichlet Distribution and Related Topics - Models and Asymptotic Behaviors

The Poisson-Dirichlet Distribution and Related Topics

Models and Asymptotic Behaviors

Feng, Shui

2010, XII, 218p.

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  • One of the first books to focus solely on the Poisson-Dirichlet distribution
  • Discusses recent progress in evolutionary dynamics and asymptotic behaviors
The Poisson-Dirichlet distribution is an infinite dimensional probability distribution. It was introduced by Kingman over thirty years ago, and has found applications in a broad range of areas including Bayesian statistics, combinatorics, differential geometry, economics, number theory, physics, and population genetics. This monograph provides a comprehensive study of this distribution and some related topics, with particular emphasis on recent progresses in evolutionary dynamics and asymptotic behaviors. One central scheme is the unification of the Poisson-Dirichlet distribution, the urn structure, the coalescent, the evolutionary dynamics through the grand particle system of Donnelly and Kurtz. It is largely self-contained. The methods and techniques used in it appeal to researchers in a wide variety of subjects.

Content Level » Research

Keywords » Coalescent - Dirichlet process - Limit theorems - Measure - Poisson process - Poisson-Dirichlet Distribution - Population Genetics - Probability and stochastic processes - Probability distribution - random measure

Related subjects » Mathematics - Probability Theory and Stochastic Processes

Table of contents / Sample pages 

Models.- The Poisson–Dirichlet Distribution.- The Two-Parameter Poisson–Dirichlet Distribution.- The Coalescent.- Stochastic Dynamics.- Particle Representation.- Asymptotic Behaviors.- Fluctuation Theorems.- Large Deviations for the Poisson–Dirichlet Distribution.- Large Deviations for the Dirichlet Processes.

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