[1] H. Abels, G.A. Margulis, G. A. Soifer, Semigroups containing proximal linear maps, Israel J. Math. 91 (1995), no. 1-3, p. 1-30. | MR | Zbl | DOI

[2] S. Adams, G.A. Eliott, T. Giordano, Amenable actions of groups, Trans. Amer. Math. Soc. 344 (1994), no. 2, p. 803-822. | MR | Zbl | DOI

[3] M. Abert, Group laws and free subgroups in topological groups (Univ. Chicago preprint 2003). | MR | Zbl

[4] M. Abert, Y. Glasner, (Univ. Chicago preprint 2003)

[5] G. Alexopoulos, Centered sub-laplacians with drift on Lie groups of polynomial volume growth, Mem. Amer. Math. Soc. 155, n. 739, (2002)

[6] G. Alexopoulos, Random walks on discrète groups of polynomial volume growth, Annals of Proba., vol 30, n. 2, (2002) p. 723-801.

[7] G. Alexopoulos, Centered densities on Lie groups of polynomial volume growth, Probab. Theory Relat. Fields 124, (2002) p. 112-150.

[8] R. Alperin. Uniform exponential growth of polycyclic groups, Geom. Dedicata 92 (2002), p. 105-113.

[9] R. Alperin, G. Noskov, Uniform growth, action on trees and $G{L}_2$, Computational and statistical group theory (Las Vegas, 2001), p. 1-5, Contemp. Math., 298, Amer. Math. Soc., 2002

[10] R. Alperin, G. Noskov, Non vanishing of algebraïc entropy for geometrically finite groups of isometries of Hadamard manifolds, (UC Berkeley preprint).

[11] N. Amosova, Local limit theorems for probabilities of moderate deviations, Lit. Mat. Sb. 14, no3. (1974), p. 401-409.

[12] C. Anantharaman, On spectral characterisations of amenability, (preprint 2003, univ. Orléans).

[13] V.I. Arnol'D et A.L. Krylov, Uniform distribution of points on a sphere and certain ergodic properties of solutions of linear ordinary differential équations in a complex domain, Dokl. Akad. Nauk SSSR 148, (1963), p. 9-12.

[14] A. Avez, Limite de quotients pour des marches aléatoires sur des groupes, C. R. Acad. Sci. Paris Sér. A-B 276 (1973), A317-A320.

[15] M. Babillot, Points entiers et groupes discrets, de l'analyse aux systèmes dynamiques, Panoramas et synthèses, (2002).

[16] P. Baldi, Caractérisation des groupes de Lie connexes récurrents, Ann. Inst. H. Poincaré Sect. B (N.S.) 17 (1981), no. 3, 281-308.

[17] P. Baldi, L. Caramelino, Large and moderate deviations for random walks on nilpotent groups, J. Theoret. Probab. 12 (1999), no. 3, p. 779-809. | MR | Zbl | DOI

[18] Y. Barnea, M. Larsen, Random generation in semi-simple algebraic groups over local fields (Univ. Indiana preprint). | MR | Zbl

[19] C. Béguin, A. Valette, A. Zuk, On the spectrum of a random walk on the discrete Heisenberg group and the norm of Harper's operator, J. Geom. and Phys. (1997), vol 21, n. 4, p. 337-356.

[20] J. Bellissard, B. Simon, Cantor spectrum for the almost Mathieu Equation, J. Funct. Anal. (1982), vol 48, n. 3, p. 408-419. | MR | Zbl | DOI

[21] Y. Benoist, Propriétés asymptotiques des groupes linéaires, GAFA, Geom. Funct. Anal. 7 (1997), p. 1-47. | MR | Zbl | DOI

[22] V. Bentkus, G. Pap, The accuracy of Gaussian approximations in nilpotent Lie groups, J. Theoret. Probab. 9 (1996), no. 4, p. 995-1017. | MR | Zbl | DOI

[23] P. Billingsley, Measure and Probability, 2ème édition. Wiley Sériés in Probability and Statistics : Probability and Statistics. John Wiley & Sons, 1999 | MR | Zbl

[24] F. Boca, A. Zaharescu, Norm estimates of almost Mathieu operators, preprint ArXiv 2003. | MR | Zbl

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

[26] A. Borel, Linear Algebraic Groups, 2nd édition, GTM 126, Springer-Verlag, (1991) 288 pp. | MR | Zbl

[27] P. Bougerol, Théorème central limite local sur certains groupes de Lie, Ann. Sci. École Norm. Sup. (4) 14 (1981), no. 4, 403-432 (1982). | MR | Zbl | Numdam | DOI

[28] P. Bougerol, J. Lacroix, Products of random matrices with applications to Schrödinger operators, Birkhäuser, Prog. in Probab. &: Stat. (1985). | MR | Zbl

[29] N. Bourbaki, Groupes et algèbres de Lie, chapitres 7 et 8, Hermann, (1975). | MR | Zbl

[30] L. Breiman, Probability, Addison-Wesley (1968). | MR | Zbl

[31] E. Breuillard, T. Gelander, On dense free subgroups of Lie groups, J. Algebra 261 (2003), no. 2, p. 448-467.

[32] E. Breuillard, T. Gelander, A topological version of Tits' alternative, (preprint 2003, chapter 7 in this dissertation).

[33] E. Breuillard, T. Gelander, Effective Tits' alternative for some linear groups, (see Appendix in this dissertation).

[34] I. D. Brown, Dual topology of a nilpotent Lie group, Ann. Sci. École Norm. Sup. (4) 6 (1973), p. 407-411.

[35] F. Bruhat, J. Tits, Groupes réductifs sur un corps local, I. Données radicielles valuées, Publ. math. IHES, 41 (1972).

[36] A. Carbery, M. Christ, J. Wright, Multidimensional van der Corput and sublevel set estimates, J. Amer. Math. Soc. 12 (1999), no. 4, p. 981-1015

[37] H. Carlsson, Error estimates in d-dimensional renewal theory, Compositio Math. 46 (1982), no. 2, 227-253.

[38] H. Carlsson, Remainder terrn estimates of the renewal function Ann. Probab. 11 (1983), no. 1, p. 143-157.

[39] Y. Carrière Feuilletages riemanniens à croissance polynômiale, Comment. Math. Helv. 63 (1988), no. 1, p. 1-20.

[40] Y. Carrière, E. Ghys, Relations d'équivalence moyennables sur les groupes de Lie, C. R. Acad. Sci. Paris Sér. I Math. 300 (1985), no. 19, p. 677-680.

[41] Y. Carrière, F. Dal'Bo, Généralisations du premier théorème de Bieberbach sur les groupes cristallographiques, Enseign. Math. (2) 35 (1989), no. 3-4, p. 245-262.

[42] G. Choquet, J. Deny, Sur l'équation de convolution $\mu =\mu *\sigma$, C. R. Acad. Sc. Paris, t. 250 (1960) p. 799-801.

[43] L. Corwin et F.P. Greenleaf, Representations of nilpotent Lie groups and their applications, Cambridge studies in advanced mathematics 18, CUP (1990).

[44] H. Cramér, Les sommes et les fonctions de variables aléatoires, Paris Hermann, (1938).

[45] H. Cramér, Elements of probability theory and some of its applications, Cambridge (1962).

[46] P. Crépel et A. Raugi, Théorème central limite sur les groupes nilpotents, Ann. Inst. H. Poincaré sect. B, Prob. & Stat., vol XIV, 2, (1978) 145-164.

[47] M. Day, Amenable semigroups, Illinois J. Math. 1 (1957), p.509-544

[48] T. Delzant, Sous-groupes distingués et quotients des groupes hyperboliques, Duke Math. J. 83 (1996), no. 3, p.661-682.

[49] J.D. Dixon, A. Mann, M.P Du Sautoy, D. Segal, Analytic pro-p groups, London Mathematical Society Lecture Note Sériés, 157. CUP, Cambridge, 1991, 251 pp.

[50] J.D. Dixon, L. Pyber, A. Seress, A. Shalev, Residual properties of free groups and probabilistic methods, J. Reine Angew. Math. 556 (2003), p.159-172.

[51] D. Dolgopyat, On mixing properties of compact group extensions of hyperbolic systems, Israel J. Math. 130 (2002), p. 157-205.

[52] E. Dynkin, M. Malioutov, Random walk on groups with a finite number of generators, Dokl. Akad. Nauk SSSR 137 (1961) p.1042-1045.

[53] D. Epstein, Almost all subgroups of a Lie group are free, J. of Algebra. 19 (1971) p. 261-262.

[54] A. Eskin, G.A. Margulis, Recurrence properties of random walks on homogeneous spaces, (preprint E. Schrodinger Institute, Vienna 2001).

[55] A. Eskin, G.A. Margulis, S. Mozes, Upper bounds and asymptotics in a quantitative version ofthe Oppenheim conjecture, Ann. of Math. (2) 147 (1998), no. 1, p. 93-141.

[56] A. Eskin, S. Mozes, H. Oh, Uniform, exponential growth for linear groups, (preprint 2003, Princeton).

[57] W. Feller, An introduction to probability theory and its applications, Vol. II. 2nd ed. John Wiley Sons, (1971).

[58] H. Furstenberg, The unique ergodicity of the horocycle flow, Recent Advances in Topological Dynamics (A. Besk ed.) Springer Verlag, 1972, p. 95-115.

[59] H. Furstenberg, Stiffness of group actions, in Lie groups and ergodic theory (Mumbai, 1996), 105-117, Tata Inst. Fund. Res. Stud. Math., 14, 1998.

[60] A. Gamburd, D. Jakobson, P. Sarnak, Spectra of elements in the group ring of SU(2), J. Eur. Math. Soc. (JEMS) 1 (1999), no. 1, 51-85.

[61] T. Gelander, A. Zuk Dependence of Kazhdan constants on generating subsets, Israel J. Math. 129 (2002) p. 93-98,

[62] E. Ghys, Groupes d'holonomie des feuilletages de Lie, Nederl. Akad. Wetensch. Indag. Math. 47 (1985), no. 2, p.173-182.

[63] E. Ghys, Riemmanian foliations : examples and problems, Appendix to the book by P. Molino Riemannian foliations Birkäuser, (1988).

[64] J. Gilman, Two-genemtor discrete subgroups of PSL(2, R), Mem. Amer. Math. Soc. 117 (1995), no. 561, 204 pp.

[65] B. Gnedenko, A. Kolmogorov, Limit distributions for sums of independent random variables, Revised edition Addison-Wesley, (1968) 293 pp.

[66] R. W. Goodman, Nilpotent Lie groups : structure and applications to analysis, LNM 562, Springer-Verlag (1976).

[67] L. Gorostiza, The central limit theorem for random, motions of d-dimensional Euclidean space, Ann. of Proba. (1973).

[68] U. Grenander, Probabilities on algebraic structures, John Wiley & Sons ; Almqvist & Wiksell, Stockholm-Göteborg-Uppsala (1963), 218 pp.

[69] R. I. Grigorchuk, Degrees of growth of finitely generated groups and the theory of invariant means, Izv. Akad. Nauk SSSR Ser. Mat. 48 (1984), no. 5, p. 939-985.

[70] M. Gromov, Hyperbolic groups, in Essays in Group Theory, p. 263, Math. Sci. Res. Inst. Publ., Springer, (1987).

[71] M. Gromov, Groups of polynomial growth and expanding maps, Publ. Math. IHES 53 (1981).

[72] Y. Guivarc'H, Générateurs des groupes résolubles, Publications des Séminaires de Mathématiques de l'Université de Rennes, 1967-1968, Exp. No. 1, 17 pp., Rennes, (1968).

[73] Y. Guivarc'H, Croissance polynomiale des groupes de Lie et périodes des fonctions harmoniques, Bull. Soc. Math. France 101, (1973), p. 333-379.

[74] Y. Guivarc'H, Equirépartition dans les espaces homogènes, Théorie ergodique (Actes Journées Ergodiques, Rennes, 1973/1974), pp. 131-142. Lecture Notes in Math., Vol. 532, Springer, Berlin, (1976).

[75] Y. Guivarc'H, M. Keane, P. Roynette, Marches aléatoires sur les groupes de Lie, LNM Vol. 624, Springer-Verlag, (1977). | MR | Zbl

[76] Y. Guivarc'H, Sur la loi des grands nombres et le rayon spectral des marches aléatoires, Conf. on Random Walks (Kleebach, 1979), 3, Astérisque, 74, (1980) p. 47-98. | MR | Zbl | Numdam

[77] Y. Guivarc'H, Marches aléatoires sur les groupes et problèmes connexes, Fascicule de probabilités, 39 pp., Publ. Inst. Rech. Math. Rennes, Univ. Rennes I, Rennes, (1993). | MR

[78] Y. Guivarc'H, Marches aléatoires sur les groupes, Development of mathematics 1950-2000, 577-608, Birkhäuser, Basel, (2000). | MR | Zbl

[79] Y. Guivarc'H, Limit theorems for random walks and products of random matrices, Lectures held at the Tata Institute, Summer School in Probab. Theory, Sept. 2002. | Zbl

[80] A. Haefliger, Feuilletages Riemanniens, Séminaire Bourbaki, Vol. 1988/89. Astérisque No. 177-178 (1989), Exp. No. 707, p. 183-197. | MR | Zbl | Numdam

[81] A. Haefliger, Groupoïdes d'holonomie et classifiants, Transversal structure of foliations (Toulouse, 1982). Astérisque No. 116 (1984), p. 70-97. | MR | Zbl | Numdam

[82] P. De La Harpe, Topics in Geometrie Group Theory, Chicago Univeritv Press, (2001). | MR | Zbl

[83] De La Harpe, P., Free Groups in Linear Groups, L'Enseignement Mathématique, 29 (1983), 129-144 | MR | Zbl

[84] P. De La Harpe, A. Valette, La propriété (T) de Kazhdan pour les groupes localement compacts, (avec un appendice de Marc Burger), Astérisque No. 175 (1989), 158 pp. | MR | Zbl | Numdam

[85] W. Hebisch, L. Saloff-Coste, Gaussian estimates for Markov chains and random walks on groups, Annals of Proba. 21 (1993) p. 673-709. | MR | Zbl

[86] W. Hebisch, A. Sikora, A smooth subadditive homogeneous norm on a homogeneous group, Studia Math. 96 (1990), no. 3, p. 231-236. | MR | Zbl | DOI

[87] H. Heyer, Probability measures on locally compact groups, Ergeb. 94 Spinger Verlag (1977). | MR | Zbl

[88] K. Hinderer, Remarks on Directly Riemann Integrable Functions, Math. Nachr. 130 (1987) p. 225-230. | MR | Zbl | DOI

[89] T. Höglund, A multi-dimensional renewal theorem, Bull. Sc. Math, 2ème série, 112 (1988) p. 111-138. | MR | Zbl

[90] G.A. Hunt, Semi-groups of measures on Lie groups, Trans. Amer. Math. Soc. 81 (1956), p. 264-293. | MR | Zbl | DOI

[91] I. Ibragimov, A central limit theorem for a class of dependent random variables, Teor. Verojatnost. i Primenen, 8, (1963), p. 89-94. | MR | Zbl

[92] J. W. Jenkins, Growth of locally compact groups, J. Functional Analysis 12 (1973), p. 113-127. | MR | Zbl | DOI

[93] T. Jorgensen, On discrete groups of Möbius transformations. Amer. J. Math. 98 (1976), no. 3, p. 739-749. | MR | Zbl | DOI

[94] W. Kantor, A. Lubotzky, The probability of generating a finite classical group, Geom. Dedicata 36 (1990), no. 1, p. 67-87. | MR | Zbl | DOI

[95] Y. Kawada, K. Itô, On the probability distribution on a compact group, I. Proc. Phys.-Math. Soc. Japan (3) 22, (1940) p. 977-998. | MR | JFM

[96] D.A. Kazhdan, Uniform distribution on a plane, Trudy Moskov. Mat. Ob. 14, (1965), p. 299-305. | MR | Zbl

[97] R. Keener, Asymptotic expansions in multivariate renewal theory, Stochastic Process. Appl. 34 (1990), no. 1, p. 137-153.

[98] H. Kesten, Symmetric random walks on groups, Trans. Amer. Math. Soc. 92, (1959), p. 336-354.

[99] A. Kirillov, Unitary representations of nilpotent Lie groups, Uspehi Mat. Nauk 17 (1962) no. 4 (106), 57-110.

[100] A. Kirillov, Éléments de la théorie des représentations, Editions Mir, Moscow, (1974) 347 pp. | MR

[101] M. Koubi, Croissance uniforme dans les groupes hyperboliques, Ann. Inst. Fourier (Grenoble) 48 (1998), no. 5, p. 1441-1453. | MR | Zbl | Numdam | DOI

[102] M. Kuranishi, On everywhere dense imbedding of free groups in Lie groups. Nagoya Math. J. 2, (1951). p. 63-71. | MR | Zbl | DOI

[103] S. Lang, Algebra, Third Edition, Addison-Wesley (1994). | Zbl

[104] E. Le Page, Théorèmes quotients pour certaines marches aléatoires, Comptes Rendus Acad. Sc., 279, série A, n. 2, (1974). | MR | Zbl

[105] E. Le Page, Un théorème local sur le groupe de Heisenberg, preprint IRMAR, Univ. Rennes 1.

[106] M. Liebeck, A. Shalev, The probability of generating a finite simple group, Geom. Dedicata 56 (1995), no. 1, p. 103-113. | MR | Zbl | DOI

[107] A. Lubotzky, Discrete groups, expanding graphs and invariant measures, with an appendix by J. D. Rogawski. Progress in Math. 125, Birkhäuser, 1994, 195 pp. | MR | Zbl

[108] A. Mann, Positively finitely generated groups,. Forum Math. 8 (1996), no. 4, p. 429-459. | MR | Zbl

[109] A. Mann, A. Shalev, Simple groups, maximal subgroups, and probabilistic aspects of profinite groups, Israel J. Math. 96 (1996), part B, p. 449-468. | MR | Zbl | DOI

[110] G.A. Margulis, Positive harmonic functions on nilpotent groups, Dokl. Akad. Nauk SSSR 166 (1966) p. 1054-1057

[111] G.A. Margulis, On the action of unipotent subgroups in the space of lattices, Mat. Sb. 86 (1971), 552-556.

[112] G.A. Margulis, Oppenheim conjecture, Fields Medallists' lectures, 272-327, World Sci. Ser. 20th Century Math., 5, World Sci. Publishing, River Edge, NJ, 1997

[113] G.A. Margulis, Random walks and Borel Harish-Chandra theorem, preprint.

[114] G. A. Margulis, Discrete subgroups of semi-simple Lie groups, Ergeb. Math. Grenz. (3) 17 Springer Verlag, (1991), 388 pp.

[115] G. A. Margulis, G.M. Tomanov, Invariant measures for actions of unipotent groups over local fields on homogeneous spaces, Invent. Math. 116 (1994), no. 1-3, p. 347-392.

[116] G. A. Margulis, G. A. Soifer, Maximal subgroups of infinité index in finitely generated linear groups, J. Algebra 69, (1981), no. 1, p. 1-23.

[117] G. Meigniez, Holonomy groups of solvable Lie foliations, in Integrable systems and foliations (Montpellier, 1995), p. 107-146, Progr. Math., 145, Birkhäuser, (1997).

[118] R. Michel, Results on probabilities of moderate deviations, Ann. Prob., no. 2 (1974), p. 349-353.

[119] J. Milnor, Growth of finitely generated solvable groups, J. Diff. Geometry 2 (1968) p. 447-449.

[120] P. Molino, Riemanman foliations, Prog. in Math. 73, Birkhäuser, (1988), 339 pp.

[121] N. Monod, Continuous bounded cohomology of loeally compact groups, LNM 1758, Springer Verlag, (2001), 214 pp.

[122] L. Mosher, Indiscrete representations, laminations, and tilings, Geometric group theory down under (Canberra, 1996), p. 225-259, de Gruyter, (1999).

[123] D. Montgomery, L. Zippin, Topological transformation groups, Reprint of the 1955 original. R. E. Krieger Publ. Co., (1974) 289 pp.

[124] A. V. Nagaev, Renewal theorems in ${ℝ}^d$, Teor. Veroyatnost. i Primenen. 24 (1979), no. 3, p. 565-573.

[125] A. V. Nagaev, Intégral limit theorems with regards to large déviations when Cramér's condition is not satisfied, Prob. Th. Appl. 14 (1969), p.51-63

[126] A. V. Nagaev, Large deviations of sums of indépendant random variables, Ann. of Prob. 7, no 5., (1979), p. 745-789.

[127] D. Neuenschwander, Probabilities on the Heisenberg group, LNM 1630, Springer-Verlag (1996).

[128] A. Nevo, preprint quoted in [12].

[129] A. Yu. Olshanskii, On the question of the existence of an invariant mean on a group, Uspekhi Mat. Nauk 35 (1980), no. 4 (214), p. 199-200.

[130] V.I. Oseledec, Markov chains, skew-products, and ergodic thoerems for "général" dynamical système, Th. Prob. &; App. (1965), 10, 3, 551-557.

[131] D. Osin. Exponential growth, solvable groups, Erg. Theory. Dyn. Sys. 23, no. 3, (2003).

[132] V. Platonov, A. Rapinchuk, Algebraic Groups and Number Theory, Academic Press, (1994).

[133] G. Pólya, Beitrag zur Verallgemeinerung des Verzerrungssatzes auf mehrfach Zusammenhangende Gebiete, S.B. Preuss. Akad. Wiss., Berlin, K.L. Math. Phys. Tech. (1928), p. 228-232 and p. 280-282.

[134] H. Poincaré, Calcul des Probabilités, 2ème éd., Gauthier Villars, (1912)

[135] L. Pyber, Group enumeration and where it leads us, Prog. in Math. Vol 169, Birkhaüser.

[136] J. F. Quint, Sous-groupes discrets des groupes semi-simples, thèse Paris VII, 2001.

[137] M. S. Raghunathan, Discrete Subgroups of Discrete Groups, Springer Verlag (1972).

[138] M. Ratner, Interaction between Ergodic Theory, Lie Groups, and Number Theory, in Proc. ICM (Zurich, 1994) 157-182, Birkhaüser, 1995.

[139] M. Ratner, On Raghunathan's measure conjecture, Ann. Math. 134 (1991), 545-607.

[140] M. Ratner, Raghunathan's topological conjecture and distributions of unipotent flows, Duke Math. J. 63 (1991), 235-290.

[141] M. Ratner, Interaction between Ergodic Theory, Lie Groups, and Number Theory, in Proc. ICM (Zurich, 1994) 157-182, Birkhaüser, 1995.

[142] A. Raugi, Théorème de la limite centrale sur les groupes Nilpotents, Z. Wahrsch. Verw. Gebiete 43 (1978), no. 2, 149-172.

[143] A. Raugi, A general Choquet-Deny theorem for a large class of locally compact second countable groups, preprint IRMAR, Univ. Rennes 1, (2002).

[144] L. Ribes, P. Zalevsskii, Profinite groups, Ergeb. Math. vol. 40, Springer Verlag (2000).

[145] H. Rubin, J. Sethuraman, Probabilities of moderate deviations, Sankhyā Ser. A, 27 (1965), p. 325-346.

[146] W. Rudin, Real and Complex Analysis, Addison-Wesley.

[147] P. Sarnak, Some applications of modular forms, Cambridge Tracts in Mathematics, 99 CUP, Cambridge, (1990)

[148] P. Scott, Subgroups of surface groups are almost geometric, J. London Math. Soc. (2) 17 (1978), no. 3, p. 555-565 erratum J. London Math. Soc. (2) 32 (1985), no. 2, p. 217-220.

[149] J.P. Serre, Lie algebras and Lie groups, Springer LNM 1500.

[150] N. Shah, Limit distributions of polynomial trajectories on homogeneous spaces, Duke Math. J. 75, 3, (1994), 711-732. | MR | Zbl | DOI

[151] N. Shah, Invariant measures and orbit closures on homogeneous spaces for actions of subgroups generated by unipotent elements. Lie groups and ergodic theory (Mumbai, 1996), 229-271, Tata Inst. Fund. Res. Stud. Math., 14, Bombay, 1998 | MR | Zbl

[152] A. Shalev, Simple groups, permutation groups, and probability, Proc. of the Inter. Cong. of Math., Vol. II (Berlin, 1998), Doc. Math. 1998, Extra Vol. II, p. 129-137. | MR | Zbl

[153] A. Shalev, Lie methods in the theory of pro-p groups, in New horizons in pro-p groups, p. 1-54, Progr. Math., 184, Birkhäuser (2000). | MR | Zbl

[154] Y. Shalom, The growth of linear groups, J. Algebra 199 (1998), no. 1, p. 169-174. | MR | Zbl | DOI

[155] G. Soifer, T. Venkataramana, Finitely generated pro-finitely dense free groups in higher rank semi-simple groups, Transform. Groups 5 (2000), no. 1. p. 93-100. | MR | Zbl | DOI

[156] E. Siebert, Absolute continuity, singularity, and supports of Gauss semigroups on a Lie group, Monat. für Math. 93, (1982), p. 239-253. | MR | Zbl | DOI

[157] E. Siebert, Densities and differentiability properties on Gauss semigroups on a Lie group, Proc. Amer. Math. Soc. vol 91, n. 2, (1984), p.298-305. | MR | Zbl | DOI

[158] A. D. Slastnikov, Limit theorems for moderate deviations probabilities, Probab. Theo. and Appl. 23 (1978), no2., p. 325-340. | Zbl | MR

[159] A. J. Stam, Renewal theory in r dimensions I. Compositio Math. 21 (1969) p. 383-399 and 23 (1971) p. 1-13. | MR | Zbl | Numdam

[160] A. N. Starkov, Dynamical systems on homogeneous spaces, Transl. of Math. Monographs, 190, AMS Prov. RI, (2000).

[161] Ch. Stone, A local limit theorem for nonlattice multi-dimensional distribution functions, Ann. Math. Stat, 36 (1965) 546-551.

[162] Ch. Stone, Ratio limit theorems for random walks on groups, Trans. Amer. Math. Soc. 125 (1966) p. 86-100. | MR | Zbl | DOI

[163] Ch. Stone, Ratio local and ratio limit theorems, 5th Berkeley Symp. on Math. Stat. and Prob., Berkeley and Los Angeles, UCP (1966), Vol II, 2, p. 217-224 | MR | Zbl

[164] Ch. Stone, Application of unsmoothing and Fourier Analysis to random walks, Markov Processes and Potential Theory, Madison Wis, (1967), p. 165-192. | MR | Zbl

[165] D. Stroock, S.R.S Varadhan, Limit theorems for random walks on Lie groups, Indian J. of Stat. Sankhyā, Ser. A, 35, (1973) p. 277-294. | MR | Zbl

[166] B. Szegedy, Communication at the conference "Groups and Probability", Budapest July 2003.

[167] J. Tits, Free subgroups in linear groups, J. Algebra 20 (1972) p. 250-270. | MR | Zbl | DOI

[168] J. Tits, Représentations linéaires irréductibles d'un groupe algébrique sur un corps quelconque, J. Reine Angew. Math. 247 (1971) p. 196-220. | MR | Zbl

[169] V.N. Tutubalin, Compositions of measures on the simplest nilpotent group, Teor. Verojatnost. i Primenen 9, 1964, p. 531-539. | MR | Zbl

[170] N. Varopoulos, Wiener-Hopf theory and nonunimodular groups, J. Funct. Anal., 120, (1994) p.467-483. | MR | Zbl | DOI

[171] N. Varopoulos, L. Saloff-Coste, et Th. Coulhon, Analysis and geometry on groups, Cambridge Tracts in Mathematics, 100, CUP, Cambridge, 1992. | MR | Zbl

[172] D. Wehn, Probabilities on Lie groups, Proc. Nat. Acad. Sci. USA, vol 48, (1962) p.791-795 | MR | Zbl | DOI

[173] D. Wehn, Limit distributions on Lie groups, Yale thesis, 1960. | MR

[174] D. Wehn, Some remarks on Gaussian Distributions on a Lie Group, Z. Wahrsch. Geb. 30, p. 255-263. | MR | Zbl | DOI

[175] W. Woess, Random walks on infinite graphs and groups, Cambridge Tracts in Mathematics, 138, CUP, Cambridge, (2000) | MR | Zbl

[176] J. Wolf, Growth of finitely generated solvable groups and curvature of Riemanniann manifolds, J. Diff. Geom. 2 (1968), p. 421-446. | MR | Zbl

[177] J. Wilson, On uniform exponential growth for solvable groups (preprint 2000).

[178] R. Zimmer, Amenable actions and dense subgroups of Lie groups, J. Funct. Anal. 72 (1987), no. 1, p. 58-64. | MR | Zbl | DOI

[179] R. Zimmer, Ergodic theory and semi-simple groups, Monographs in Math., 81, Birkhäuser Verlag, (1984), 209 pp. | MR | Zbl

[180] R. Zimmer, Amenable ergodic group actions and an application to Poisson boundaries of random walks, J. Funct. Anal. 27 (1978), no. 3, p. 350-372. | MR | Zbl | DOI

[181] R. Zimmer, Kazhdan groups acting on compact manifolds, Invent. Math. 75 (1984), no. 3, p. 425-436. | MR | Zbl | DOI

[182] R. Zimmer, Amenable pairs of groups and ergodic actions and the associated von Neumann algebras, Trans. Amer. Math. Soc. 243 (1978), 271-286. | MR | Zbl | DOI