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The Poisson-Dirichlet Distribution and Related Topics

Models and Asymptotic Behaviors

  • Book
  • © 2010

Overview

Authors:
  1. Shui Feng

    1. Dept. Mathematics & Statistics, McMaster University, Hamilton, Canada

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  • First book to our knowledge that solely treats the Poisson-Dirichlet distribution
  • Focuses also on recent progresses in evolutionary dynamics and asymptotic behaviors
  • Reviewed by international experts
  • Includes supplementary material: sn.pub/extras

Part of the book series: Probability and Its Applications (PIA)

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Table of contents (9 chapters)

  1. Front Matter

    Pages I-XIII
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  2. Models

    1. Front Matter

      Pages 1-1
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    2. Introduction

      • Shui Feng
      Pages 3-14

    3. The Poisson–Dirichlet Distribution

      • Shui Feng
      Pages 15-52

    4. The Two-Parameter Poisson–Dirichlet Distribution

      • Shui Feng
      Pages 53-66

    5. The Coalescent

      • Shui Feng
      Pages 67-80

    6. Stochastic Dynamics

      • Shui Feng
      Pages 81-112

    7. Particle Representation

      • Shui Feng
      Pages 113-124

  3. Asymptotic Behaviors

    1. Front Matter

      Pages 125-125
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    2. Fluctuation Theorems

      • Shui Feng
      Pages 127-150

    3. Large Deviations for the Poisson–Dirichlet Distribution

      • Shui Feng
      Pages 151-178

    4. Large Deviations for the Dirichlet Processes

      • Shui Feng
      Pages 179-197

  4. Back Matter

    Pages 199-218
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Keywords

About this book

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.

Reviews

From the reviews:

“The intended audience of this book includes researchers and graduate students in probability, population genetics and statistics. Most material in the book is self-contained and should be accessible to anyone with a graduate level knowledge of probability theory. … this book provides useful connections to mathematical population genetics and many advanced probabilistic applications.” (Wenbo V. Li, Mathematical Reviews, Issue 2012 c)

Authors and Affiliations

  • Dept. Mathematics & Statistics, McMaster University, Hamilton, Canada

    Shui Feng

About the author

Shui Feng is a Professor of Mathematics and Statistics at McMaster University, Canada. His research is in the broad area of stochastic processes and limit theorems, with particular interests in stochastic models in population genetics, finance, and statistical physics. He is the co-editor of one book and the author of more than 30 research papers.

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