Actions of large semigroups and random walks on isometric extensions of boundaries
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 40 (2007) no. 2, pp. 209-249.
@article{ASENS_2007_4_40_2_209_0,
     author = {Guivarc'h, Yves and Raugi, Albert},
     title = {Actions of large semigroups and random walks on isometric extensions of boundaries},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {209--249},
     publisher = {Elsevier},
     volume = {Ser. 4, 40},
     number = {2},
     year = {2007},
     doi = {10.1016/j.ansens.2007.01.003},
     mrnumber = {2339285},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.ansens.2007.01.003/}
}
TY  - JOUR
AU  - Guivarc'h, Yves
AU  - Raugi, Albert
TI  - Actions of large semigroups and random walks on isometric extensions of boundaries
JO  - Annales scientifiques de l'École Normale Supérieure
PY  - 2007
SP  - 209
EP  - 249
VL  - 40
IS  - 2
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/j.ansens.2007.01.003/
DO  - 10.1016/j.ansens.2007.01.003
LA  - en
ID  - ASENS_2007_4_40_2_209_0
ER  - 
%0 Journal Article
%A Guivarc'h, Yves
%A Raugi, Albert
%T Actions of large semigroups and random walks on isometric extensions of boundaries
%J Annales scientifiques de l'École Normale Supérieure
%D 2007
%P 209-249
%V 40
%N 2
%I Elsevier
%U http://archive.numdam.org/articles/10.1016/j.ansens.2007.01.003/
%R 10.1016/j.ansens.2007.01.003
%G en
%F ASENS_2007_4_40_2_209_0
Guivarc'h, Yves; Raugi, Albert. Actions of large semigroups and random walks on isometric extensions of boundaries. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 40 (2007) no. 2, pp. 209-249. doi : 10.1016/j.ansens.2007.01.003. http://archive.numdam.org/articles/10.1016/j.ansens.2007.01.003/

[1] Abels H., Margulis G.A., Soifer G.A., Semigroups containing proximal linear maps, Israel J. Math. 91 (1995) 1-30. | MR | Zbl

[2] Arnold L., Random Dynamical Systems, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 1998. | MR | Zbl

[3] Baker A., Transcendental Number Theory, Cambridge Univ. Press, Cambridge, UK, 1975, x+147 pp. | MR | Zbl

[4] Benoist Y., Propriétés asymptotiques des groupes linéaires II, in: Analysis on Homogeneous Spaces and Representation Theory of Lie Groups, Okayama-Kyoto, 1997, Adv. Stud. Pure Math., vol. 26, Math. Soc. Japan, Tokyo, 2000, pp. 33-48. | MR | Zbl

[5] Benoist Y., Convexes divisibles III, Annales Scient. É.N.S. 38 (5) (2005) 793-832. | Numdam | MR | Zbl

[6] Benoist Y., Labourie F., Sur les difféomorphismes d'Anosov affines à feuilletages stable et instable différentiables, Invent. Math. 111 (1993) 285-308. | MR | Zbl

[7] Benoist Y., Automorphismes des cones convexes, Invent. Math. 141 (2000) 149-193. | MR | Zbl

[8] Borel A., Introduction aux groupes arithmétiques, Hermann, Paris, 1969. | MR | Zbl

[9] Borel A., Linear Algebraic Groups, G.T.M., vol. 126, second ed., Springer-Verlag, New York, 1996. | MR | Zbl

[10] Bougerol P., Lacroix J., Products of Random Matrices and Applications to Schrödinger Operators with Random Potential, in: Progress in Probability Theory and Math. Statistics, vol. 8, Birkhäuser, Boston, 1985. | MR | Zbl

[11] Conze J.P., Guivarc'H Y., Densité d'orbites d'actions de groupes linéaires et propriétés d'équidistribution de marches aléatoires, in: Burger M., Iozzi A. (Eds.), Rigidity in Dynamics and Geometry, Cambridge, 2000, Springer-Verlag, Berlin, 2002, 39-76. | Zbl

[12] Dolgopyat D., On mixing properties of compact group extensions of hyperbolic systems, Israel J. Math. 130 (2002) 157-2005. | MR | Zbl

[13] Ferte D., Flot horosphérique des repères sur les variétés hyperboliques de dimension 3 et spectre des groupes kleiniens, Bull. Brazilian Math. Soc. 33 (1) (2002) 99-123. | MR | Zbl

[14] Furstenberg H., Boundary theory and stochastic processes on homogeneous spaces, in: Moore C.C. (Ed.), Harmonic Analysis on Homogeneous Spaces, Proc. Symp. Pure Math., vol. 26, Amer. Math. Soc., Providence, RI, 1972, pp. 193-229. | MR | Zbl

[15] Goldsheid I., Guivarc'H Y., Zariski Closure and the dimension of the Gaussian law of the product of random matrices I, P.T.R.F. 105 (1996) 109-142. | MR | Zbl

[16] Guivarc'H Y., Produits de matrices aléatoires et applications aux propriétés géométriques des sous-groupes du groupe linéaire, Ergodic Theory Dynam. Systems 10 (1990) 129-131. | MR | Zbl

[17] Guivarc'H Y., Raugi A., Frontière de Furstenberg, propriétés de contraction et théorèmes de convergence, Z. Wahrsch. Verw. Gebiete 69 (2) (1985) 187-242. | MR | Zbl

[18] Guivarc'H Y., Raugi A., Contraction properties of an invertible matrix semigroup, Lyapunov coefficients of a product of independent random matrices, Israel J. Math. 65 (2) (1989) 165-196. | MR | Zbl

[19] Guivarc'H Y., Renewal theorems, product of random matrices, and toral endomorphisms, in: Potential Theory in Matsue, Adv. Stud. Pure Math. Math. Soc. Japan, vol. 44, 2006, pp. 53-66. | MR | Zbl

[20] Guivarc'H Y., Starkov A., Orbits of linear group actions, random walks on homogeneous spaces and toral automorphisms, Ergodic Theory Dynam. Systems 24 (2004) 767-802. | MR | Zbl

[21] Karlin S., Total Positivity, vol. I, Stanford Univ. Press, Stanford, CA, 1968. | MR | Zbl

[22] Ledrappier F., Pollicott M., Ergodic properties of linear actions of 2×2 matrices, Duke Math. J. 116 (2) (2003) 353-388. | MR | Zbl

[23] Margulis G.A., Problems and conjectures in rigidity theory, in: Mathematics Frontiers and Perspectives, Amer. Math. Soc., Providence, RI, 2000, pp. 161-174. | MR | Zbl

[24] Mumford D., Algebraic Geometry, Complex Projective Varieties, Grundlehren Der Mathematischen Wissenschaften, vol. 221, Springer-Verlag, Berlin/New York, 1976. | MR | Zbl

[25] Onischik A.L., Vinberg E.B., Lie Groups and Algebraic Groups, Springer-Verlag, Berlin/New York, 1990. | MR | Zbl

[26] Prasad G., R-regular elements in Zariski-dense subgroups, Quart. J. Math. Oxford, 2 45 (180) (1994) 541-545. | MR | Zbl

[27] Prasad G., Rapinchuk A., Zariski-dense subgroups and transcendental number theory, Math. Res. Lett. 12 (2-3) (2005) 239-249. | Zbl

[28] Prasad G., Rapinchuk A., Existence of irreducible R-regular elements in Zariski-dense subgroups, Math. Res. Lett. 10 (2003) 21-32. | MR | Zbl

[29] Raugi A., Théorie spectrale d'un opérateur de transition sur un espace métrique compact, Ann. Inst. H. Poincaré 28 (2) (1992) 281-309, (Fascicule de probabilités, 21 pp., Publ. Inst. Rech. Math. Rennes, 1994, Univ. Rennes I, Rennes, 1994). | Numdam | MR | Zbl

[30] Raugi A., Théorème ergodique multiplicatif, Produits de matrices aléatoires indépendantes, Fascicule de probabilités, 43 pp., Publ. Inst. Rech. Math. Rennes, 1996/1997. | Zbl

[31] Raugi A., Fonctions harmoniques et théorèmes limites pour les marches aléatoires sur les groupes, Bull. Soc. Math. France 54 (1977) 5-118. | Numdam | MR | Zbl

[32] Rosenblatt M., Equicontinuous Markov operators, Teor. Verojatnost. i Primenen. 9 (1964) 205-222. | MR | Zbl

[33] Salem R., On some singular monotonic function which are strictly increasing, TAMS 53 (1943) 427-439. | MR | Zbl

[34] Witte D., Co-compact subgroups of semi-simple Lie groups, in: Benkart G.M., Osborn J.M. (Eds.), Lie Algebras and Related Topics, Contemp. Math., vol. 110, 1990, pp. 309-313. | Zbl

[35] Zimmer R., Ergodic Theory and Semi-Simple Lie Groups, Monographs in Math., vol. 81, Birkhäuser-Verlag, Basel, 1984. | MR | Zbl

Cité par Sources :