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  3. Harmonic Analysis on Finite Groups
  • Cited by 72
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    • Publisher:
      Cambridge University Press
      Publication date:
      December 2009
      March 2008
      ISBN:
      9780511619823
      9780521883368
      DOI:
      https://doi.org/10.1017/CBO9780511619823
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.722kg, 454 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics (general), Mathematics, Abstract Analysis, Algebra
      Series:
      Cambridge Studies in Advanced Mathematics (108)
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    Subjects:
    Mathematics (general), Mathematics, Abstract Analysis, Algebra
    Series:
    Cambridge Studies in Advanced Mathematics (108)
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    Book description

    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.

    Reviews

    '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.'

    Source: 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.'

    Source: EMS Newsletter

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