Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-26T01:10:50.362Z Has data issue: false hasContentIssue false
  • English
  • Français

Produits de matrices aléatoires et applications aux propriétés géometriques des sous-groupes du groupe linéaire

Published online by Cambridge University Press:  19 September 2008

Yves Guivarc'h
Yves Guivarc'h
Affiliation:
Université de Paris VI, Laboratoire de Probabilités, Tour 56–3e étage, 4, Place Jussieu, 75252 Paris Cedex 05, France
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Using the asymptotic properties of products of random matrices we study some properties of the subgroups of the linear group. These properties are centered around the theorem of J. Tits giving the existence of free subgroups in linear groups.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 10 , Issue 3 , September 1990 , pp. 483 - 512
Copyright
Copyright © Cambridge University Press 1990

References

REFERENCES

[1]Bougerol, P. & Lacroix, J.. Products of Random Matrices with Applications to Schrödinger Operators. Birkhauser: 1986.Google Scholar
[2]Chevalley, C.. Théorie des Groupes de Lie. Hermann: 1968.Google Scholar
[3]Cohen, J., Kesten, H. & Newman, C., eds., Random matrices and applications. Contemp. Math. Amer. Math. Soc. 50 (1986).Google Scholar
[4]Dixon, J. D.. Free subgroups of linear groups, pp. 45–56. Lecture Notes in Math. 319 Springer: 1973.Google Scholar
[5]Furstenberg, H.. Boundary theory and stochastic processes on homogeneous spaces. Proc. Symp. Pure Math. 6 (1972), 193–229.Google Scholar
[6]Glaner, S.. Proximal flows. Springer Lecture Notes 517 (1976).Google Scholar
[7]Goldsheid, I. & Margulis, G. A.. Simplicity of the Liapunoff spectrum for products of random matrices. 35 (1987), 309–313.Google Scholar
[8]Guimier, F.. Simplicité du spectre de Liapunoff d'un produit de matrices aléatoires sur un corps ultramétrique. C.R.A.S. Paris (1989), (à paraître).Google Scholar
[9]Guivarc'h, Y.. Quelques propriétés asymptotiques des produits de matrices aléatoires. Springer Lecture Notes 774 (1980) 176–250.Google Scholar
[10]Guivarc'h, Y. & Raugi, A.. Frontière de Furstenberg, propriétés de contraction et théorèmes de convergence. Z. Wahr. 69 (1985) 187–242.Google Scholar
[11]Guivarc'h, Y.. Croissance polynomiale et périodes des fonctions harmoniques. Bulletin Soc. Math. France 101 (1973), 333–379.Google Scholar
[12]Guivarc'h, Y. & Raugi, A.. Propriétés de contraction d'un semi–groupe de matrices inversibles. Israël J. Math. 65 (2) (1989), 165–196.Google Scholar
[13]Guivarc'h, Y. & Raugi, A.. Quelques remarques sur les produits de matrices aléatoires indépendantes. C.R.A.S. 304 série 1, 8 (1987), 199–201.Google Scholar
[14]de la Harpe, P.. Free groups in linear groups. L'Enseignement Math. 29 (1983), 129–144.Google Scholar
[15]de la Harpe, P.. Reduced C*–algebras of discrete groups which are simple with a unique trace. pp. 248–251. Lecture Notes 1132 Springer–Verlag.Google Scholar
[16]Ledrappier, F.. Poisson boundaries of discrete groups of matrices. Israël J. Math. 50 (4) (1985).Google Scholar
[17]Le Page, E.. Théorèmes limites pour les produits de matrices aléatoires. Springer Lecture Notes 928 (1982), 258–303.Google Scholar
[18]Margulis, G. A.. Arithméticity of the irreductible lattices in the semi–simple groups of rank greater than one. Invent. Math. 76 (1984), 93–120.Google Scholar
[19]Margulis, G. A. & Soifer, G. A.. A criterion for the existence of maximal subgroups of infinite index in a finitely generated linear group. Soviet Math. Dokl. 18 (3) (1977), 847–851.Google Scholar
[20]Moore, C. C.. Amenable subgroups of semi–simple groups and proximal flows. Israël J. Math. 34 (1979), 121–138.Google Scholar
[21]Raghunathan, M. S.. A proof of Oseledet multiplicative theorem. Israël J. Math. 32 (1979) 356–362.Google Scholar
[22]Sullivan, D.. The density at infinity of a discrete group of hyperbolic motions. Publ. Math. I.H.E.S. 50.Google Scholar
[23]Tits, J.. Free subgroups in linear groups. J. of Algebra 20 (1972), 250–270.Google Scholar
[24]Wehrfritz, B. A. F.. Infinite linear groups. Ergebnisse der Mathemalik (1973).CrossRefGoogle Scholar
[25]Weil, A.. Basic number theory. Grundlehren der Math Wiss. 144 Springer: 1967.Google Scholar
[26]Zimmer, R.. Ergodic theory and semi–simple groups. Birkhauser: 1984.CrossRefGoogle Scholar