Titlebook: Random Walks on Reductive Groups; Yves Benoist,Jean-François Quint Book 2016 Springer International Publishing AG 2016 Markov chain.Martin

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Regularity of the Stationary Measure prove the Law of Large Numbers for the coefficients and for the spectral radius. We also prove the Central Limit Theorem, Law of Iterated Logarithm and Large Deviation Principle for the norm of matrices, the norm of vectors, the coefficients and the spectral radius.

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Book 2016 - 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..

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Random Walks on Reductive Groups978-3-319-47721-3Series ISSN 0071-1136 Series E-ISSN 2197-5655

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Introduction,The introduction is a dialog between the reader and the authors explaining the content of the book in a light style and in an easily understandable language.

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Stationary MeasuresWe recall basic facts on Markov chains, their invariant probability measures and their . dynamical system. We also recall the Markov chains associated to a random walk and their . dynamical system.

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The Law of Large NumbersWe prove the Law of Large Numbers for a real valued cocycle over a semigroup action.

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