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Catalogue Information
Field name	Details
Dewey Class	519.2
Title	Random Walks on Reductive Groups ([EBook]) / by Yves Benoist, Jean-François Quint.
Author	Benoist, Yves
Added Personal Name	Quint, Jean-François author.
Other name(s)	SpringerLink (Online service)
Publication	Cham : : Springer International Publishing : : Imprint: Springer, , 2016.
Physical Details	XI, 323 p. : online resource.
Series	Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics 0071-1136 ; ; 62
ISBN	9783319477213
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-319-47721-3
Links to Related Works	Subject References: Dynamical systems and ergodic theory . Dynamics . Ergodic theory . Lie groups . Mathematics . Probabilities . Probability theory and stochastic processes . Topological groups . Topological groups, Lie groups . Authors: Benoist, Yves . Quint, Jean-François . Corporate Authors: SpringerLink (Online service) . Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics . Classification: 519.2 .

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Random Walks on Reductive Groups

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