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Random Walks on Reductive Groups

Yves Benoist, Jean-François Quint

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ca. 53,49 €
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Springer International Publishing img Link Publisher

Naturwissenschaften, Medizin, Informatik, Technik / Wahrscheinlichkeitstheorie, Stochastik, Mathematische Statistik

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.

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Schlagwörter

Essential spectrum, Local Limit Theorem, Law of Large Numbers, Central Limit Theorem, Stationary measure, Lyapunov exponents, Markov chain, Martingale, Algebraic group