Harmonic Analysis on Finite Groups
Harmonic Analysis on Finite Groups
Fabio Scarabotti , Università degli Studi di Roma 'La Sapienza', Italy
Filippo Tolli , Università degli Studi Roma Tre
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$131.00
USDStarting 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 self-contained, detailed study culminates with case-by-case analyses of the cut-off phenomenon discovered by Persi Diaconis.
- 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 fully-worked 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 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
Product details
March 2008Hardback
9780521883368
454 pages
234 × 160 × 25 mm
0.722kg
76 b/w illus. 5 tables 140 exercises
Available
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 Laplace-Bernoulli 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.
