LEADER 04113nam 22006375 450 001 9910136092203321 005 20200702111052.0 010 $a3-319-47721-8 024 7 $a10.1007/978-3-319-47721-3 035 $a(CKB)3710000000915546 035 $a(DE-He213)978-3-319-47721-3 035 $a(MiAaPQ)EBC4722274 035 $a(PPN)196323703 035 $a(EXLCZ)993710000000915546 100 $a20161020d2016 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aRandom Walks on Reductive Groups /$fby Yves Benoist, Jean-François Quint 205 $a1st ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016. 215 $a1 online resource (XI, 323 p.) 225 1 $aErgebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics,$x0071-1136 ;$v62 311 $a3-319-47719-6 320 $aIncludes bibliographical references and index. 327 $aIntroduction -- 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. 330 $aThe classical theory of random walks describes the asymptotic behavior of sums of independent identically distributed random real variables. This book explains the generalization of this theory to products of independent identically distributed random matrices with real coefficients. Under the assumption that the action of the matrices is semisimple ? or, equivalently, that the Zariski closure of the group generated by these matrices is reductive - and under suitable moment assumptions, it is shown that the norm of the products of such random matrices satisfies a number of classical probabilistic laws. This book includes necessary background on the theory of reductive algebraic groups, probability theory and operator theory, thereby providing a modern introduction to the topic. 410 0$aErgebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics,$x0071-1136 ;$v62 606 $aProbabilities 606 $aDynamics 606 $aErgodic theory 606 $aTopological groups 606 $aLie groups 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 606 $aTopological Groups, Lie Groups$3https://scigraph.springernature.com/ontologies/product-market-codes/M11132 615 0$aProbabilities. 615 0$aDynamics. 615 0$aErgodic theory. 615 0$aTopological groups. 615 0$aLie groups. 615 14$aProbability Theory and Stochastic Processes. 615 24$aDynamical Systems and Ergodic Theory. 615 24$aTopological Groups, Lie Groups. 676 $a519.282 700 $aBenoist$b Yves$4aut$4http://id.loc.gov/vocabulary/relators/aut$0756055 702 $aQuint$b Jean-François$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910136092203321 996 $aRandom Walks on Reductive Groups$92162741 997 $aUNINA