Actions of large semigroups and random walks on isometric extensions of boundaries

Yves Guivarc'h; Albert Raugi

Annales scientifiques de l'École Normale Supérieure (2007)

  • Volume: 40, Issue: 2, page 209-249
  • ISSN: 0012-9593

How to cite


Guivarc'h, Yves, and Raugi, Albert. "Actions of large semigroups and random walks on isometric extensions of boundaries." Annales scientifiques de l'École Normale Supérieure 40.2 (2007): 209-249. <>.

author = {Guivarc'h, Yves, Raugi, Albert},
journal = {Annales scientifiques de l'École Normale Supérieure},
language = {eng},
number = {2},
pages = {209-249},
publisher = {Elsevier},
title = {Actions of large semigroups and random walks on isometric extensions of boundaries},
url = {},
volume = {40},
year = {2007},

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
PB - Elsevier
VL - 40
IS - 2
SP - 209
EP - 249
LA - eng
UR -
ER -


  1. [1] Abels H., Margulis G.A., Soifer G.A., Semigroups containing proximal linear maps, Israel J. Math.91 (1995) 1-30. Zbl0845.22004MR1348303
  2. [2] Arnold L., Random Dynamical Systems, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 1998. Zbl0906.34001MR1723992
  3. [3] Baker A., Transcendental Number Theory, Cambridge Univ. Press, Cambridge, UK, 1975, x+147 pp. Zbl0297.10013MR422171
  4. [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. Zbl0960.22012MR1770716
  5. [5] Benoist Y., Convexes divisibles III, Annales Scient. É.N.S.38 (5) (2005) 793-832. Zbl1085.22006MR2195260
  6. [6] Benoist Y., Labourie F., Sur les difféomorphismes d'Anosov affines à feuilletages stable et instable différentiables, Invent. Math.111 (1993) 285-308. Zbl0777.58029MR1198811
  7. [7] Benoist Y., Automorphismes des cones convexes, Invent. Math.141 (2000) 149-193. Zbl0957.22008MR1767272
  8. [8] Borel A., Introduction aux groupes arithmétiques, Hermann, Paris, 1969. Zbl0186.33202MR244260
  9. [9] Borel A., Linear Algebraic Groups, G.T.M., vol. 126, second ed., Springer-Verlag, New York, 1996. Zbl0726.20030MR1102012
  10. [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. Zbl0572.60001MR886674
  11. [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. Zbl1012.37006
  12. [12] Dolgopyat D., On mixing properties of compact group extensions of hyperbolic systems, Israel J. Math.130 (2002) 157-2005. Zbl1005.37005MR1919377
  13. [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. Zbl1031.37032MR1934285
  14. [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. Zbl0289.22011MR352328
  15. [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. Zbl0854.60006MR1389734
  16. [16] Guivarc'h Y., Produits de matrices aléatoires et applications aux propriétés géométriques des sous-groupes du groupe linéaire, Ergodic Theory Dynam. Systems10 (1990) 129-131. Zbl0715.60008MR1074315
  17. [17] Guivarc'h Y., Raugi A., Frontière de Furstenberg, propriétés de contraction et théorèmes de convergence, Z. Wahrsch. Verw. Gebiete69 (2) (1985) 187-242. Zbl0558.60009MR779457
  18. [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. Zbl0677.60007MR998669
  19. [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. Zbl1119.37008MR2277822
  20. [20] Guivarc'h Y., Starkov A., Orbits of linear group actions, random walks on homogeneous spaces and toral automorphisms, Ergodic Theory Dynam. Systems24 (2004) 767-802. Zbl1050.37012MR2060998
  21. [21] Karlin S., Total Positivity, vol. I, Stanford Univ. Press, Stanford, CA, 1968. Zbl0219.47030MR230102
  22. [22] Ledrappier F., Pollicott M., Ergodic properties of linear actions of 2 × 2 matrices, Duke Math. J.116 (2) (2003) 353-388. Zbl1020.37009MR1953296
  23. [23] Margulis G.A., Problems and conjectures in rigidity theory, in: Mathematics Frontiers and Perspectives, Amer. Math. Soc., Providence, RI, 2000, pp. 161-174. Zbl0952.22005MR1754775
  24. [24] Mumford D., Algebraic Geometry, Complex Projective Varieties, Grundlehren Der Mathematischen Wissenschaften, vol. 221, Springer-Verlag, Berlin/New York, 1976. Zbl0456.14001MR453732
  25. [25] Onischik A.L., Vinberg E.B., Lie Groups and Algebraic Groups, Springer-Verlag, Berlin/New York, 1990. Zbl0722.22004MR1064110
  26. [26] Prasad G., R -regular elements in Zariski-dense subgroups, Quart. J. Math. Oxford, 245 (180) (1994) 541-545. Zbl0828.22010MR1315463
  27. [27] Prasad G., Rapinchuk A., Zariski-dense subgroups and transcendental number theory, Math. Res. Lett.12 (2–3) (2005) 239-249. Zbl1072.22009
  28. [28] Prasad G., Rapinchuk A., Existence of irreducible R -regular elements in Zariski-dense subgroups, Math. Res. Lett.10 (2003) 21-32. Zbl1029.22020MR1960120
  29. [29] Raugi A., Théorie spectrale d'un opérateur de transition sur un espace métrique compact, Ann. Inst. H. Poincaré28 (2) (1992) 281-309, (Fascicule de probabilités, 21 pp., Publ. Inst. Rech. Math. Rennes, 1994, Univ. Rennes I, Rennes, 1994). Zbl0752.60054MR1162576
  30. [30] Raugi A., Théorème ergodique multiplicatif, Produits de matrices aléatoires indépendantes, Fascicule de probabilités, 43 pp., Publ. Inst. Rech. Math. Rennes, 1996/1997. Zbl0947.60008
  31. [31] Raugi A., Fonctions harmoniques et théorèmes limites pour les marches aléatoires sur les groupes, Bull. Soc. Math. France54 (1977) 5-118. Zbl0389.60003MR517392
  32. [32] Rosenblatt M., Equicontinuous Markov operators, Teor. Verojatnost. i Primenen.9 (1964) 205-222. Zbl0133.40101MR171318
  33. [33] Salem R., On some singular monotonic function which are strictly increasing, TAMS53 (1943) 427-439. Zbl0060.13709MR7929
  34. [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. Zbl0733.22010
  35. [35] Zimmer R., Ergodic Theory and Semi-Simple Lie Groups, Monographs in Math., vol. 81, Birkhäuser-Verlag, Basel, 1984. Zbl0571.58015MR776417

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