Probability Measures on Semigroups

Convolution Products, Random Walks and Random Matrices

  • Göran Högnäs
  • Arunava Mukherjea
Part of the Probability and Its Applications book series (PIA)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Göran Högnäs, Arunava Mukherjea
    Pages 1-62
  3. Göran Högnäs, Arunava Mukherjea
    Pages 63-169
  4. Göran Högnäs, Arunava Mukherjea
    Pages 171-251
  5. Göran Högnäs, Arunava Mukherjea
    Pages 253-358
  6. Back Matter
    Pages 359-430

About this book

Introduction

Semigroups are very general structures and scientists often come across them in various contexts in science and engineering. In this second edition of Probability Measures on Semigroups, first published in the University Series in Mathematics in 1996, the authors present the theory of weak convergence of convolution products of probability measures on semigroups, the theory of random walks on semigroups, and their applications to products of random matrices. They examine the essentials of abstract semigroup theory and its application to concrete semigroups of matrices. They present results on weak convergence, random walks, random matrices using semigroup ideas that for the most part are complete and best possible. Still, as the authors point out, there are other results that remain to be completed. These are all mentioned in the notes and comments at the end of each chapter, and will keep the readership of this book enthusiastic and interested for some time to come. Apart from corrections of several errors, new results have been added in the main text and in the appendices; the references, all notes and comments at the end of each chapter have been updated, and exercises have been added. This volume is suitable for a one semester course on semigroups and it could be used as a main text or supplementary material for courses focusing on probability on algebraic structures or weak convergence. It is ideally suited to graduate students in mathematics, and in other fields such as engineering and sciences with an interest in probability. Students in statistics using advance probability will also find it useful. 'A well-written book...This is elegant mathematics, motivated by examples and presented in an accessible way that engages the reader.' International Statistics Institute, December 1996 'This beautiful book...guides the reader through the most important developments...a valuable addition to the library of the probabilist, and a must for anybody interested in probability on algebraic structures.' Zentralblatt für Mathematik und ihre Grenzgebiete-Mathematical Abstracts 'This well-written volume, by two of the most successful workers in the field....deserves to become the standard introduction for beginning researchers in this field.' Journal of the Royal Statistical Society

Authors and affiliations

  • Göran Högnäs
    • 1
  • Arunava Mukherjea
    • 2
  1. 1.Department of MathematicsÅbo Akademi UniversityÅboFinland
  2. 2.Deptartment MathematicsUniversity of Texas-Pan AmericanEdinburgUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-77548-7
  • Copyright Information Springer Science+Business Media, LLC 2011
  • Publisher Name Springer, Boston, MA
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-77547-0
  • Online ISBN 978-0-387-77548-7
  • Series Print ISSN 1431-7028
  • About this book