Zariski closure and the dimension of the Gaussian law of the product of random matrices. I

Probability Theory and Related Fields

Volumn 105, Issue 1, 1996, Pages 109-142

  Goldsheid, I Ya ^a   Guivarc'h, Y ^b  

^a QUEEN MARY UNIVERSITY OF LONDON   (United Kingdom)

^b UNIVERSITÉ DE RENNES 1   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030542449     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01192073     Document Type: Article

References (35)

1. Bougerol P., Lacroix J.: Products of Random Matrices with Applications to Schrödinger Operators. Boston Basel Stuttgart: Birkhäuser 1985
2. Chevalley C,: Theory of Lie Groups. Princeton: Princetor University Press 1965
3. Furstenberg H.: Kesten H.: Products of random matrices. Ann. Math. Statist 31, 457-469 (1960)
4. Furstenberg H.: Non commuting random products. Trans. Amer. Math. Soc. 108, 337-428 (1963)
5. Furstenberg H.: Boundary theory and stochastic processes on homogeneous spaces. Proc. Symp. Pure Math. pp. 193-229. (1972).
6. Goldsheid I.Ya.: Lyapunov exponents and asymptotic behaviour of the product of random matrices. Lecture Notes in Math., Vol. 1486, pp. 23-37. (1991)
7. Goldsheid I.Ya.: Zariski Closure of Subgroups of the Symplectic Group and Lyapunov Exponents of the Schrödinger Operator on the Strip. Comm. Math. Phys. 174, 347-365 (1995)
8. Goldsheid I.Ya.: Quasi-prjective transformations. I, (Preprint)
9. Goldsheid I.Ya.: Asymptotic properties of the product of random matrices depending on a parameter, in: Ya. G. Sinai and R. L. Dobrushin. (eds) 'Multicomponent Random Systems'. New York Basel: Dekker 1980 pp.239-283.
10. Goldsheid I.Ya., Guivarc'h Y. Dimension de la loi gaussienne pour un produit de matrices aléatoires indépendantes et adhérence de Zariski. C. R. Acad. Sci. Paris, 313, Série I, 305-308 (1991)
11. Goldsheid I.Ya., Margulis G.A.: Conditions for simplicity of the spectrum of Lyapunov indices. Dokl. Akad. Nauk SSSR 293, 297-301 (1987); Soviet Math. Dokl. 35, 309-313 (1987)
12. Goldsheid I.Ya., Margulis G.A.: Conditions for simplicity of the spectrum of Lyapunov indices. Dokl. Akad. Nauk SSSR 293, 297-301 (1987); Soviet Math. Dokl. 35, 309-313 (1987)
13. Goldsheid I.Ya., Margulis G.A.: Lyapunov indices of products of random matrices. Uspekhi Mat. Nauk 44(5), 13-60 (1989); Russian Math. Surveys 44(5), 11-71 (1989),
14. Goldsheid I.Ya., Margulis G.A.: Lyapunov indices of products of random matrices. Uspekhi Mat. Nauk 44(5), 13-60 (1989); Russian Math. Surveys 44(5), 11-71 (1989),
15. Guivarc'h Y.: Quelques propriétés asymptotiques des produits de matrices aléatoires. Lecture Notes in Math., Vol. 774 pp. 176-250. Berlin: Springer 1980
16. Guivarc'h Y.: Sur les exposants de Liapunov des marches aleatoires. C.R.A.S., 292, 327-329 (1981)
17. Guivarc'h Y.: Produits de matrices aléatoires et applications aux propriétés géométriques des sous-groupes du groupe linéaire. Ergodic Theory and Dynamical Systems 10, 483-512 (1990),
18. Guivarc'h Y., Raugi A.: Frontiere de Furstenberg, propriétés de contraction et théorémes de convergence. Z. Wahr. Theorie 69, 187-242 (1985)
19. Guivarc'h Y., Raugi A.: Products of random matrices: convergence theorems. Contemporary Math. 50 31-54 (1986)
20. Guivarc'h Y., Raugi A.: Propriété de contraction d'un semigroupe de matrices inversibles. Coefficients de Liapunoff d'un Produit de matrices aléatoires indépendantes. Israel J. Math. 65(2) 165-196 (1989)
21. Kaijser T.: A limit theorem for Markov chains on compact metric spaces with application to products of random matrices. Duke Math. J. 45 311-349 (1978)
22. Kaijser T.: On distribution problems for random products of non-commutative matrices. Report 22, Uppsala University, 1970.
23. Kingman J.F.S.: Subadditive Processes. In: Ecole d'Eté de Probabilités de Saint-Flour V, Lecture Notes in Math. Vol. 539 pp. 167-233 Berlin: Springer (1976)
24. Ledrapier F.: Quelques propriétés des exposants caractéristiques. Ecole d'Eté de Probabilites de Saint Flour. Lect. Notes in. Math., Vol. 1097. Berlin: Springer 1984.
25. Le Page E.: Théorèmes limites pour les produits de matrices aléatoires. Lecture Notes in Math., Vol. 928 pp. 258-303. Berlin: Springer 1982
26. Nagaev S.V.: Some limit theorems for stationary Markov chains. Theory Probab. Appl. 2 378-406 (1957)
27. Onishchik A. L. and Vinberg E. B.: Lie Groups and Algebraic Groups. Berlin Heidelberg New York: Spr nger 1990
28. Oseledets V.I.: A multiplicative ergodic theorem. Characteristic Lyapunov exponents of dynamical systems, Trudy Moskov. Mat. Obshch. 19 179-210 (1968); Trans. Moscow Math. Soc. 19, 197-231 (1968)
29. Oseledets V.I.: A multiplicative ergodic theorem. Characteristic Lyapunov exponents of dynamical systems, Trudy Moskov. Mat. Obshch. 19 179-210 (1968); Trans. Moscow Math. Soc. 19, 197-231 (1968)
30. Raugi A.: Fonctions harmoniques et théorèmes limites sur les groupes. Bull. SMF, mem. 54, 1977.
31. Ruelle D.: Characteristic exponents and invariant manifolds in Hubert space. Ann. Math., Ser.2, 115(2), 243-290, (1982).
32. Tutubalin V.N.: Limit theorems for a product of random matrices. Teor. Veroyatnost. i Primenen. 10, 19-32 (1965); Theory Probab. Appl. 10, 15-27 (1965)
33. Tutubalin V.N.: Limit theorems for a product of random matrices. Teor. Veroyatnost. i Primenen. 10, 19-32 (1965); Theory Probab. Appl. 10, 15-27 (1965)
34. Tutubalin V.N.: The central limit theorem for products of random matrices and some applications. Symposia Math., 21, pp. 101-116. New York: Academic Press 1977.
35. Virtser A.D.: Central limiting theorem for semi-simple Lie groups. Theory Probab. Appl. 15 667-687 (1970)