Random Walks on Reductive Groups, 1st ed. 2016 Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics Series, Vol. 62
Langue : Anglais
Auteurs : Benoist Yves, Quint Jean-François
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.
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.
Provides a self-contained introduction to the products of independent identically distributed random matrices and to their Lyapunov exponents
Explains the relevance of the theory of reductive algebraic groups and the theory of bounded operators in Banach spaces to the study of random matrices
Contains a proof of the Local Limit Theorem for the norm of the products of independent identically distributed random matrices
Includes supplementary material: sn.pub/extras
Date de parution : 11-2016
Ouvrage de 323 p.
15.5x23.5 cm
Date de parution : 06-2018
Ouvrage de 323 p.
15.5x23.5 cm
Thème de Random Walks on Reductive Groups :
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