Harmonic analysis on finite groups : representation theory, Gelfand pairs and Markov chains
著者
書誌事項
Harmonic analysis on finite groups : representation theory, Gelfand pairs and Markov chains
（Cambridge studies in advanced mathematics, 108）
Cambridge University Press, 2008
- : hardback
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注記
Includes bibliographical references (p. 421-432) and index
内容説明・目次
内容説明
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.
目次
- 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.
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