Representation Theory, Gelfand Pairs and Markov Chains
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Köp båda 2 för 1563 kr'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.