- Inbunden (Hardback)
- Antal sidor
- illustrated ed
- Cambridge University Press
- Scarabotti, Fabio / Tolli, Filippo
- 76 line diagrams 5 tables 140 exercises 76 figures 65 worked examples
- Series Number 108 Harmonic Analysis on Finite Groups: Representation Theory, Gelfand Pairs and Markov Chains
- 229 x 150 x 28 mm
- Antal komponenter
- 14:B&W 6 x 9 in or 229 x 152 mm Case Laminate on White w/Gloss Lam
- 545 g
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Harmonic Analysis on Finite Groups
Representation Theory, Gelfand Pairs and Markov Chains839
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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.
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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.' 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
Tullio Ceccherini-Silberstein is Professor of Mathematical Analysis in the Department of Engineering at the Universit... del Sannio, Benevento. Fabio Scarabotti is Professor of Mathematical Analysis in the Department of Mathematics at the Universit... degli Studi di Roma 'La Sapienza'. Filippo Tolli is Assistant Professor of Mathematical Analysis in the Department of Mathematics at the Universit... Roma Tre.
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 qanalogs; 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.