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

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.

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)

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.

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.

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