Table of contents
About this book
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.
Markov chain Martingale Stationary measure Law of Large Numbers Lyapunov exponents Algebraic group Central Limit Theorem Local Limit Theorem Essential spectrum
- DOI https://doi.org/10.1007/978-3-319-47721-3
- Copyright Information Springer International Publishing AG 2016
- Publisher Name Springer, Cham
- eBook Packages Mathematics and Statistics
- Print ISBN 978-3-319-47719-0
- Online ISBN 978-3-319-47721-3
- Series Print ISSN 0071-1136
- Series Online ISSN 2197-5655
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