Harmonic Analysis on Finite Groups: Representation Theory, Gelfand Pairs and Markov Chains: 108 (Cambridge Studies in Advanced Mathematics, Series Number 108)

by Fabio Scarabotti (Author), Filippo Tolli (Author), Tullio Ceccherini-Silberstein (Author)

New
Hardcover
2008
$124.13

Line up a deck of 52 cards on a table. Randomly choose two cards and switch them. How many switches are needed in order to mix up the deck? Starting from a few concrete problems such as random walks on the discrete circle and the finite ultrametric space this book develops the necessary tools for the asymptotic analysis of these processes. This detailed study culminates with the case-by-case analysis of the cut-off phenomenon discovered by Persi Diaconis. This self-contained text is ideal for graduate students and researchers working in the areas of representation theory, group theory, harmonic analysis and Markov chains. Its topics range from the basic theory needed for students new to this area, to advanced topics such as the theory of Green's algebras, the complete analysis of the random matchings, and the representation theory of the symmetric group.

Synopsis

Line up a deck of 52 cards on a table. Randomly choose two cards and switch them. How many switches are needed in order to mix up the deck? Starting from a few concrete problems such as random walks on the discrete circle and the finite ultrametric space this book develops the necessary tools for the asymptotic analysis of these processes. This detailed study culminates with the case-by-case analysis of the cut-off phenomenon discovered by Persi Diaconis. This self-contained text is ideal for graduate students and researchers working in the areas of representation theory, group theory, harmonic analysis and Markov chains. Its topics range from the basic theory needed for students new to this area, to advanced topics such as the theory of Green's algebras, the complete analysis of the random matchings, and the representation theory of the symmetric group.

$124.13

Quantity

20+ in stock

More Information

Format: Hardcover
Pages: 454
Edition: 1
Publisher: Cambridge University Press
Published: 06 Mar 2008
ISBN 10: 0521883369
ISBN 13: 9780521883368
Book Overview: Self-contained text, ideal for graduate students new to the area and researchers.

Media Reviews

'Starting from a few concrete problems such as random walks on the discrete circle and the finite ultrametric space, this book develops the necessary tools for the asymptotic analysis of these processes.' The Times Higher Education Supplement
'There are not many books that can be used both as an elementary textbook and a research monograph with the same ease and success. This one ... is a rare example. ... No prerequisites on probability theory and Markov chains are required; everything is explained in detail. From a researcher's point of view, the introduction and detailed study of Gelfand pairs in the context of finite groups is very valuable. ... The book can be warmly recommended for anyone interested in the subject and/or looking for interesting applications of representation theory.' EMS Newsletter
This book is, as far as I know, the first treatise fully devoted to finite Gel'fand pairs and their applications to probability and combinatories. ... It has lots of worked-out examples, and dozens of exercises (the solutions of which can be found in Appendix 2). Alain Valette, Mathematical Reviews
This is the perfect group theory resource for probability theory students. D.V. Feldman, University of New Hampshire for Choice Magazine

Author Bio

Tullio Ceccherini-Silberstein is Professor of Mathematical Analysis in the Department of Engineering at the Universita del Sannio, Benevento. Fabio Scarabotti is Professor of Mathematical Analysis in the Department of Mathematics at the Universita degli Studi di Roma 'La Sapienza'. Filippo Tolli is Assistant Professor of Mathematical Analysis in the Department of Mathematics at the Universita Roma Tre.