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    Taylor, Samuel J. and Tiozzo, Giulio 2016. Random Extensions of Free Groups and Surface Groups are Hyperbolic. International Mathematics Research Notices, Vol. 2016, Issue. 1, p. 294.


    Girko, V. L. and Vladimirova, A. I. 2009. Spectral analysis of stochastic recurrence systems of growing dimension under G-condition. Canonical equation K 91. Random Operators and Stochastic Equations, Vol. 17, Issue. 3,


    Bourgain, Jean and Gamburd, Alex 2008. Random walks and expansion in. Comptes Rendus Mathematique, Vol. 346, Issue. 11-12, p. 619.


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  • Ergodic Theory and Dynamical Systems, Volume 10, Issue 3
  • September 1990, pp. 483-512

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

  • Yves Guivarc'h (a1)
  • DOI: http://dx.doi.org/10.1017/S0143385700005708
  • Published online: 01 September 2008
Abstract
Abstract

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.

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[3]J. Cohen , H. Kesten & C. Newman , eds., Random matrices and applications. Contemp. Math. Amer. Math. Soc. 50 (1986).

[12]Y. Guivarc'h & A. Raugi . Propriétés de contraction d'un semi–groupe de matrices inversibles. Israël J. Math. 65 (2) (1989), 165196.

[18]G. A. Margulis . Arithméticity of the irreductible lattices in the semi–simple groups of rank greater than one. Invent. Math. 76 (1984), 93120.

[20]C. C. Moore . Amenable subgroups of semi–simple groups and proximal flows. Israël J. Math. 34 (1979), 121138.

[21]M. S. Raghunathan . A proof of Oseledet multiplicative theorem. Israël J. Math. 32 (1979) 356362.

[23]J. Tits . Free subgroups in linear groups. J. of Algebra 20 (1972), 250270.

[26]R. Zimmer . Ergodic theory and semi–simple groups. Birkhauser: 1984.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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