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Viser: Random Walks on Reductive Groups
Random Walks on Reductive Groups Vital Source e-bog
Yves Benoist
(2016)
Random Walks on Reductive Groups
Yves Benoist og Jean-François Quint
(2016)
Sprog: Engelsk
Detaljer om varen
- Vital Source searchable e-book (Fixed pages)
- Udgiver: Springer Nature (Oktober 2016)
- ISBN: 9783319477213
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Detaljer om varen
- 1. Udgave
- Hardback
- Udgiver: Springer International Publishing AG (November 2016)
- Forfattere: Yves Benoist og Jean-François Quint
- ISBN: 9783319477190
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.
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.