Random Walks on Reductive Groups

Nonfiction, Science & Nature, Mathematics, Mathematical Analysis, Statistics
Cover of the book Random Walks on Reductive Groups by Yves Benoist, Jean-François Quint, Springer International Publishing
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Author: Yves Benoist, Jean-François Quint ISBN: 9783319477213
Publisher: Springer International Publishing Publication: October 20, 2016
Imprint: Springer Language: English
Author: Yves Benoist, Jean-François Quint
ISBN: 9783319477213
Publisher: Springer International Publishing
Publication: October 20, 2016
Imprint: Springer
Language: English

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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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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