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Random Walks on Reductive Groups

  • Yves Benoist
  • Jean-François Quint

Table of contents

  1. Front Matter
    Pages I-XI
  2. Yves Benoist, Jean-François Quint
    Pages 1-16
  3. The Law of Large Numbers

    1. Front Matter
      Pages 17-17
    2. Yves Benoist, Jean-François Quint
      Pages 19-36
    3. Yves Benoist, Jean-François Quint
      Pages 37-49
    4. Yves Benoist, Jean-François Quint
      Pages 51-75
    5. Yves Benoist, Jean-François Quint
      Pages 77-86
  4. Reductive Groups

    1. Front Matter
      Pages 87-87
    2. Yves Benoist, Jean-François Quint
      Pages 89-113
    3. Yves Benoist, Jean-François Quint
      Pages 115-126
    4. Yves Benoist, Jean-François Quint
      Pages 127-145
    5. Yves Benoist, Jean-François Quint
      Pages 147-152
    6. Yves Benoist, Jean-François Quint
      Pages 153-167
  5. The Central Limit Theorem

    1. Front Matter
      Pages 169-169
    2. Yves Benoist, Jean-François Quint
      Pages 171-189
    3. Yves Benoist, Jean-François Quint
      Pages 191-202
    4. Yves Benoist, Jean-François Quint
      Pages 203-222
    5. Yves Benoist, Jean-François Quint
      Pages 223-245
  6. The Local Limit Theorem

    1. Front Matter
      Pages 247-247
    2. Yves Benoist, Jean-François Quint
      Pages 249-258
    3. Yves Benoist, Jean-François Quint
      Pages 259-272
    4. Yves Benoist, Jean-François Quint
      Pages 273-285
  7. Back Matter
    Pages 287-323

About this book

Introduction

The classical theory of random walks describes the asymptotic behavior of sums of independent identically distributed random real variables. This book explains the generalization of this theory to products of independent identically distributed random matrices with real coefficients.

Under the assumption that the action of the matrices is semisimple – or, equivalently, that the Zariski closure of the group generated by these matrices is reductive - and under suitable moment assumptions, it is shown that the norm of the products of such random matrices satisfies a number of classical probabilistic laws.

This book includes necessary background on the theory of reductive algebraic groups, probability theory and operator theory, thereby providing a modern introduction to the topic.

Keywords

Markov chain Martingale Stationary measure Law of Large Numbers Lyapunov exponents Algebraic group Central Limit Theorem Local Limit Theorem Essential spectrum

Authors and affiliations

  • Yves Benoist
    • 1
  • Jean-François Quint
    • 2
  1. 1.Université Paris-Sud OrsayFrance
  2. 2.Institut de Mathématiques de BordeauxUniversité Bordeaux 1 Talence CedexFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-47721-3
  • Copyright Information Springer International Publishing AG 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-47719-0
  • Online ISBN 978-3-319-47721-3
  • Series Print ISSN 0071-1136
  • Series Online ISSN 2197-5655
  • Buy this book on publisher's site
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