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OverviewThe 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. Full Product DetailsAuthor: Yves Benoist , Jean-François QuintPublisher: Springer International Publishing AG Imprint: Springer International Publishing AG Edition: 1st ed. 2016 Volume: 62 Weight: 6.878kg ISBN: 9783319477190ISBN 10: 3319477196 Pages: 323 Publication Date: 01 November 2016 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of ContentsIntroduction.- 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.ReviewsBenoist 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) Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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