The Poisson-Dirichlet Distribution and Related Topics

丛 书 名：Probability and Its Applications

版本说明：1

作     者：Shui Feng 

I S B N：(纸本) 9783642111938;9783642263798 

出 版 社：Springer Berlin  Heidelberg 

出 版 年：1000年

页      数：XIV, 218页

主 题 词：Probability Theory and Stochastic Processes Mathematical Modeling and Industrial Mathematics Mathematical and Computational Biology 

摘      要：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.