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Random Walks on Reductive Groups
Buch von Jean-François Quint (u. a.)
Sprache: Englisch

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Beschreibung
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.
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.
Zusammenfassung

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

Inhaltsverzeichnis
Introduction.- Part I The Law of Large Numbers.- Stationary measures.- The Law of Large Numbers.- Linear random walks.- Finite index subsemigroups.- Part II Reductive groups.- Loxodromic elements.- The Jordan projection of semigroups.- Reductive groups and their representations.- Zariski dense subsemigroups.- Random walks on reductive groups.- Part III The Central Limit Theorem.- Transfer operators over contracting actions.- Limit laws for cocycles.- Limit laws for products of random matrices.- Regularity of the stationary measure.- Part IV The Local Limit Theorem.- The Spectrum of the complex transfer operator.- The Local limit theorem for cocycles.- The local limit theorem for products of random matrices.- Part V Appendix.- Convergence of sequences of random variables.- The essential spectrum of bounded operators.- Bibliographical comments.
Details
Erscheinungsjahr: 2016
Fachbereich: Wahrscheinlichkeitstheorie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 336
Reihe: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Inhalt: xi
323 S.
ISBN-13: 9783319477190
ISBN-10: 3319477196
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Quint, Jean-François
Benoist, Yves
Auflage: 1st ed. 2016
Hersteller: Springer International Publishing
Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Maße: 241 x 160 x 23 mm
Von/Mit: Jean-François Quint (u. a.)
Erscheinungsdatum: 01.11.2016
Gewicht: 0,731 kg
preigu-id: 107768914
Zusammenfassung

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

Inhaltsverzeichnis
Introduction.- Part I The Law of Large Numbers.- Stationary measures.- The Law of Large Numbers.- Linear random walks.- Finite index subsemigroups.- Part II Reductive groups.- Loxodromic elements.- The Jordan projection of semigroups.- Reductive groups and their representations.- Zariski dense subsemigroups.- Random walks on reductive groups.- Part III The Central Limit Theorem.- Transfer operators over contracting actions.- Limit laws for cocycles.- Limit laws for products of random matrices.- Regularity of the stationary measure.- Part IV The Local Limit Theorem.- The Spectrum of the complex transfer operator.- The Local limit theorem for cocycles.- The local limit theorem for products of random matrices.- Part V Appendix.- Convergence of sequences of random variables.- The essential spectrum of bounded operators.- Bibliographical comments.
Details
Erscheinungsjahr: 2016
Fachbereich: Wahrscheinlichkeitstheorie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 336
Reihe: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Inhalt: xi
323 S.
ISBN-13: 9783319477190
ISBN-10: 3319477196
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Quint, Jean-François
Benoist, Yves
Auflage: 1st ed. 2016
Hersteller: Springer International Publishing
Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Maße: 241 x 160 x 23 mm
Von/Mit: Jean-François Quint (u. a.)
Erscheinungsdatum: 01.11.2016
Gewicht: 0,731 kg
preigu-id: 107768914
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