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Harmonic Analysis on Finite Groups
Representation Theory, Gelfand Pairs and Markov Chains

$111.00 (C)

Part of Cambridge Studies in Advanced Mathematics

  • Date Published: March 2008
  • availability: Available
  • format: Hardback
  • isbn: 9780521883368

$ 111.00 (C)

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About the Authors
  • 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 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
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    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

    See more 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: 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

  • Authors

    Tullio Ceccherini-Silberstein, Università degli Studi del Sannio, Benevento
    Tullio Ceccherini-Silberstein is Professor of Mathematical Analysis in the Department of Engineering at the Università del Sannio, Benevento.

    Fabio Scarabotti, Università degli Studi di Roma 'La Sapienza', Italy
    Fabio Scarabotti is Professor of Mathematical Analysis in the Department of Mathematics at the Università degli Studi di Roma 'La Sapienza'.

    Filippo Tolli, Università degli Studi Roma Tre
    Filippo Tolli is Assistant Professor of Mathematical Analysis in the Department of Mathematics at the Università Roma Tre.

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