The Poisson-Dirichlet Distribution and Related Topics - Models 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.

List of contents

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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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)

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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)

Product details

• Authors: Shui Feng
• Publisher: Springer, Berlin
• Languages: English
• Product format: Hardback
• Released: 09.07.2010
• EAN: 9783642111938
• ISBN: 978-3-642-11193-8
• No. of pages: 218
• Dimensions: 165 mm x 17 mm x 239 mm
• Weight: 468 g
• Illustrations: XIV, 218 p.
• Series: Probability and Its Applications; Probability and Its Applications
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics; Stochastik, B, Mathematik für Ingenieure, DV-gestützte Biologie/Bioinformatik, Mathematische Modellierung, Mathematics and Statistics, Probability Theory and Stochastic Processes, Probabilities, Stochastics, Probability Theory, Maths for scientists, Maths for engineers, Mathematical modelling, Mathematical Modeling and Industrial Mathematics, Mathematical models, Biomathematics, Mathematical and Computational Biology