Harmonic Analysis on Finite Groups
Representation Theory, Gelfand Pairs and Markov Chains
$90.00 (C)
Part of Cambridge Studies in Advanced Mathematics
 Authors:
 Tullio CeccheriniSilberstein, Università degli Studi del Sannio, Benevento
 Fabio Scarabotti, Università degli Studi di Roma 'La Sapienza', Italy
 Filippo Tolli, Università degli Studi Roma Tre
 Date Published: March 2008
 availability: In stock
 format: Hardback
 isbn: 9780521883368
$90.00 (C)
Hardback
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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. 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 a presentation of the presentation theory of the symmetric group. This selfcontained, detailed study culminates with casebycase analyses of the cutoff phenomenon discovered by Persi Diaconis.
Read more Can be used as a textbook for advanced undergraduate and graduate students, and as a reference for researchers
 First book with a complete treatment of the theory of Gelfand pairs
 Contains 140 exercises, with solutions or generous hints, and over 60 fullyworked examples
Reviews & endorsements
"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 workedout examples, and dozens of exercises (the solutions of which can be found in Appendix 2)."
Alain Valette, Mathematical ReviewsSee more reviews"This is the perfect group theory resource for probability theory students."
D.V. Feldman, University of New Hampshire for Choice MagazineCustomer reviews
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×Product details
 Date Published: March 2008
 format: Hardback
 isbn: 9780521883368
 length: 454 pages
 dimensions: 234 x 160 x 25 mm
 weight: 0.722kg
 contains: 76 b/w illus. 5 tables 140 exercises
 availability: In stock
Table of Contents
Part I. Preliminaries, Examples and Motivations:
1. Finite Markov chains
2. Two basic examples on Abelian groups
Part II. Representation Theory and Gelfand Pairs:
3. Basic representation theory of finite groups
4. Finite Gelfand pairs
5. Distance regular graphs and the Hamming scheme
6. The Johnson Scheme and the LaplaceBernoulli diffusion model
7. The ultrametric space
Part III. Advanced theory:
8. Posets and the q−analogs
9. Complements on representation theory
10. Basic representation theory of the symmetric group
11. The Gelfand Pair (S2n, S2 o Sn) and random matchings
Appendix 1. The discrete trigonometric transforms
Appendix 2. Solutions of the exercises
Bibliography
Index.