Random Walks on Reductive Groups
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 assum...
| Main Authors: | , |
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| Format: | eBook |
| Language: | English |
| Published: |
Cham
Springer International Publishing
2016, 2016
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| Edition: | 1st ed. 2016 |
| Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- Introduction
- Part I The Law of Large Numbers
- Stationary measures
- The Law of Large Numbers
- Linear random walks
- Finite index subsemigroups
- Part II Reductive groups
- Loxodromic elements
- The Jordan projection of semigroups
- Reductive groups and their representations
- Zariski dense subsemigroups
- Random walks on reductive groups
- Part III The Central Limit Theorem
- Transfer operators over contracting actions
- Limit laws for cocycles
- Limit laws for products of random matrices
- Regularity of the stationary measure
- Part IV The Local Limit Theorem
- The Spectrum of the complex transfer operator
- The Local limit theorem for cocycles
- The local limit theorem for products of random matrices
- Part V Appendix
- Convergence of sequences of random variables
- The essential spectrum of bounded operators
- Bibliographical comments