Random Walks on Reductive Groups / Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics Bd.62 (PDF)
(Sprache: Englisch)
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...
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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.
Bibliographische Angaben
- Autoren: Yves Benoist , Jean-François Quint
- 2016, 1st ed. 2016, 323 Seiten, Englisch
- Verlag: Springer-Verlag GmbH
- ISBN-10: 3319477218
- ISBN-13: 9783319477213
- Erscheinungsdatum: 20.10.2016
Abhängig von Bildschirmgröße und eingestellter Schriftgröße kann die Seitenzahl auf Ihrem Lesegerät variieren.
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- Dateiformat: PDF
- Größe: 2.44 MB
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Englisch
Pressezitat
“Benoist and Quint have written an excellent text, one that will surely become a standard reference to introduce students to the fascinating nonabelian extension of the now-classical study of random walks. … I congratulate the authors on their well-written and timely offering, and strongly recommend that libraries order a copy of this excellent text!” (Tushar Das, MAA Reviews, November, 2017)“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)
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