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Random Walks on Reductive Groups. 1st ed. 2016.
・ISBN 978-3-319-47719-0 hard EUR 139.99
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| 著者・編者 | Benoist, Yves / Quint, Jean-Francois, |
|---|---|
| シリーズ | Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics |
| 出版社 | (Springer International Publishing AG, SZ) |
| 出版年月 | 2016 |
| ページ数 | 323 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-24594＞ |
解説
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.
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.