Probability and Its Applications

Probability Measures on Semigroups

Convolution Products, Random Walks and Random Matrices

Authors: Högnäs, Göran, Mukherjea, Arunava

  • Presents up-to-date material
  • Examines abstract semigroup theory and its application to concrete semigroups of matrices
  • Includes exercises at various levels
  • Includes the best available proofs on the most important theorems used in a book

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About this book

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

Reviews

From the reviews of the second edition:

`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 Royal Statistical Society

“Högnäs and Mukherjea have made substantial contributions to the subject themselves and present their work and that of others in a unified way. … For students … this book is an excellent account of the long-term behavior of random transformations. It organizes the ideas very well and its development of the theory is clear and rigorous. … a useful reference for anyone interested in random walks on semigroups and groups. … will be valuable to any reader who wishes to learn the subject … .” (George Willis, SIAM Review, Vol. 54 (2), 2012)


Table of contents (4 chapters)

  • Semigroups

    Högnäs, Göran (et al.)

    Pages 1-62

  • Probability Measures on Topological Semigroups

    Högnäs, Göran (et al.)

    Pages 63-169

  • Random Walks on Semigroups

    Högnäs, Göran (et al.)

    Pages 171-251

  • Random Matrices

    Högnäs, Göran (et al.)

    Pages 253-358

Buy this book

eBook $139.00
price for USA (gross)
  • ISBN 978-0-387-77548-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $179.00
price for USA
  • ISBN 978-0-387-77547-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $179.00
price for USA
  • ISBN 978-1-4614-2732-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Probability Measures on Semigroups
Book Subtitle
Convolution Products, Random Walks and Random Matrices
Authors
Series Title
Probability and Its Applications
Copyright
2011
Publisher
Springer US
Copyright Holder
Springer Science+Business Media, LLC
eBook ISBN
978-0-387-77548-7
DOI
10.1007/978-0-387-77548-7
Hardcover ISBN
978-0-387-77547-0
Softcover ISBN
978-1-4614-2732-2
Series ISSN
1431-7028
Edition Number
2
Number of Pages
XII, 430
Topics