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On Products of Random Matrices and Operators

1980; Society for Industrial and Applied Mathematics; Volume: 24; Issue: 2 Linguagem: Inglês

10.1137/1124040

1095-7219

A. D. Virtser,

Mathematical Dynamics and Fractals

Previous article Next article On Products of Random Matrices and OperatorsA. D. VirtserA. D. Virtserhttps://doi.org/10.1137/1124040PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] H. Furstenberg and , H. Kesten, Products of random matrices, Ann. Math. Statist, 31 (1960), 457–469 MR0121828 (22:12558) 0137.35501 CrossrefGoogle Scholar[2] Harry Furstenberg, Noncommuting random products, Trans. Amer. Math. Soc., 108 (1963), 377–428 MR0163345 (29:648) 0203.19102 CrossrefGoogle Scholar[3] L. A. Pastur, On the spectrum of random Jacobian matrices and Schrödinger equations with random potential on the entire axis, 1974, Preprint, FTINT Akad. Nauk Ukrain. SSR, Khar'kov, (In Russian.) Google Scholar[4] M. M. Benderskii˘ and , L. A. Pastur, The asymptotic behavior of the solutions of a second order equation with random coefficients, Teor. Funkcii˘ Funkcional. Anal. i Priložen., (1975), 3–14, 160, (In Russian.) MR0394876 (52:15675) Google Scholar[5] Christian Berg and , Jens Peter Reus Christensen, On the relation between amenability of locally compact groups and the norms of convolution operators, Math. Ann., 208 (1974), 149–153 10.1007/BF01432382 MR0340963 (49:5713) 0264.43003 CrossrefGoogle Scholar[6] Yves Derriennic and , Yves Guivarc'h, Théorème de renouvellement pour les groupes non moyennables, C. R. Acad. Sci. Paris Sér. A-B, 277 (1973), A613–A615 MR0328990 (48:7332) 0272.60005 Google Scholar[7] V. I. Oseledets, A multiplicative ergodic theorem. Characteristic Ljapunov, exponents of dynamical systems, Trudy Moskov. Mat. Obšč., 19 (1968), 179–210 MR0240280 (39:1629) 0236.93034 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Exponential Growth of Products of Non-Stationary Markov-Dependent MatricesInternational Mathematics Research Notices, Vol. 2022, No. 8 | 12 October 2021 Cross Ref Random walks on hyperbolic spaces: Concentration inequalities and probabilistic Tits alternativeProbability Theory and Related Fields, Vol. 160 | 4 March 2022 Cross Ref A regularity method for lower bounds on the Lyapunov exponent for stochastic differential equationsInventiones mathematicae, Vol. 227, No. 2 | 13 September 2021 Cross Ref Lyapunov Exponents for Random Perturbations of Coupled Standard MapsCommunications in Mathematical Physics, Vol. 329 | 16 November 2021 Cross Ref Parametric Furstenberg Theorem on random products of SL(2,R) matricesAdvances in Mathematics, Vol. 378 | 1 Feb 2021 Cross Ref Lyapunov exponents for random perturbations of some area-preserving maps including the standard mapAnnals of Mathematics, Vol. 185, No. 1 | 1 January 2017 Cross Ref Multivariate Statistical Analysis and Random Matrix TheoryStochastic Models, Information Theory, and Lie Groups, Volume 2 | 29 September 2011 Cross Ref Exponential decay of correlations for randomly chosen hyperbolic toral automorphismsChaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 17, No. 4 | 1 Dec 2007 Cross Ref The Thouless formula for random non-Hermitian Jacobi matricesIsrael Journal of Mathematics, Vol. 148, No. 1 | 1 Dec 2005 Cross Ref Constant Q and a Fractal, Stratified EarthSeismic Waves in Laterally Inhomogeneous Media | 1 Jan 2002 Cross Ref Chapter 12 Random walks on groups and random transformationsHandbook of Dynamical Systems | 1 Jan 2002 Cross Ref Surface Stretching for Ornstein Uhlenbeck Velocity FieldsElectronic Communications in Probability, Vol. 2, No. none | 1 Jan 1997 Cross Ref Topological classification of linear hyperbolic cocyclesJournal of Dynamics and Differential Equations, Vol. 8, No. 3 | 1 Jul 1996 Cross Ref Positive Lyapunov exponents for a class of deterministic potentialsCommunications in Mathematical Physics, Vol. 168, No. 3 | 1 Apr 1995 Cross Ref Extremal exponents of random dynamical systems do not vanishJournal of Dynamics and Differential Equations, Vol. 2, No. 3 | 1 Jul 1990 Cross Ref Lyapunov exponents and relative entropy for a stochastic flow of diffeomorphismsProbability Theory and Related Fields, Vol. 81, No. 4 | 1 May 1989 Cross Ref Furstenberg's theorem for nonlinear stochastic systemsProbability Theory and Related Fields, Vol. 74, No. 4 | 1 Apr 1987 Cross Ref Positivity of the exponent for stationary sequences of matricesLyapunov Exponents | 17 September 2006 Cross Ref Coarse-Grained Quantities and Local Environment Effects in Disordered Systems. 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VirtserTheory of Probability & Its Applications, Vol. 28, No. 1 | 17 July 2006AbstractPDF (1239 KB)Stochastic Systems: Qualitative Theory and Lyapunov ExponentsFluctuations and Sensitivity in Nonequilibrium Systems | 1 Jan 1984 Cross Ref Random schrödinger operatorsÉcole d'Été de Probabilités de Saint Flour XIV - 1984 Cross Ref Volume 24, Issue 2| 1980Theory of Probability & Its Applications241-452 History Submitted:10 January 1977Published online:28 July 2006 InformationCopyright © 1979 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1124040Article page range:pp. 367-377ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics