Authors:
- Provides a self-contained introduction to the products of independent identically distributed random matrices and to their Lyapunov exponents
- Explains the relevance of the theory of reductive algebraic groups and the theory of bounded operators in Banach spaces to the study of random matrices
- Contains a proof of the Local Limit Theorem for the norm of the products of independent identically distributed random matrices
- Includes supplementary material: sn.pub/extras
Part of the book series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics (MATHE3, volume 62)
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Table of contents (17 chapters)
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Front Matter
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The Law of Large Numbers
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Front Matter
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The Central Limit Theorem
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Front Matter
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The Local Limit Theorem
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Front Matter
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About this book
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.
Reviews
“This book is an exposition of the tools and perspectives needed to reach the current frontier of research in the field of random matrix products… This is a technical subject, drawing on tools from a diverse range of topics… The authors take time to explain everything at a reasonable pace.” (Radhakrishnan Nair, Mathematical Reviews)
“This reviewer does not hesitate to consider this book as exceptional.” (Marius Iosifescu, zbMATH, 1366.60002)
Authors and Affiliations
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Université Paris-Sud , Orsay, France
Yves Benoist
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Institut de Mathématiques de Bordeaux, Université Bordeaux 1 , Talence Cedex, France
Jean-François Quint
Bibliographic Information
Book Title: Random Walks on Reductive Groups
Authors: Yves Benoist, Jean-François Quint
Series Title: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
DOI: https://doi.org/10.1007/978-3-319-47721-3
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2016
Hardcover ISBN: 978-3-319-47719-0Published: 01 November 2016
Softcover ISBN: 978-3-319-83805-2Published: 29 June 2018
eBook ISBN: 978-3-319-47721-3Published: 20 October 2016
Series ISSN: 0071-1136
Series E-ISSN: 2197-5655
Edition Number: 1
Number of Pages: XI, 323
Topics: Probability Theory and Stochastic Processes, Dynamical Systems and Ergodic Theory, Topological Groups, Lie Groups