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9780521883368

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

by
  • ISBN13:

    9780521883368

  • ISBN10:

    0521883369

  • Edition: 1st
  • Format: Hardcover
  • Copyright: 2008-03-17
  • Publisher: Cambridge University Press

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Summary

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.

Table of Contents

Preliminaries, Examples and Motivations
Finite Markov chains
Two basic examples on Abelian groups
Representation Theory and Gelfand Pairs
Basic representation theory of finite groups
Finite Gelfand pairs
Distance regular graphs and the Hamming scheme
The Johnson Scheme and the Laplace-Bernoulli diffusion model
The ultrametric space
Advanced theory
Posets and the q-analogs
Complements on representation theory
Basic representation theory of the symmetric group
The Gelfand Pair (S2n, S2 o Sn) and random matchings
The discrete trigonometric transforms
Solutions of the exercises
Bibliography
Index
Table of Contents provided by Publisher. All Rights Reserved.

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The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

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