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

top

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. <http://eudml.org/doc/82712>.

@article{Guivarch2007,
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 = {http://eudml.org/doc/82712},
volume = {40},
year = {2007},
}

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
PB - Elsevier
VL - 40
IS - 2
SP - 209
EP - 249
LA - eng
UR - http://eudml.org/doc/82712
ER -

References

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.