Marches aléatoires sur les groupes

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1. [A-K] V.I. Arnold, A.L. Krylov - Uniform distribution of points on a sphere and some ergodic properties of solutions of differential equations in a complex region, Sov. Math Dokl4 n° 1, p 1-5, 1963. Zbl0237.34008
2. (Ah) Alhfors - Conformal invariants. Topics in geometric function theory, Mac Graw Hill, New York, 1973. Zbl0272.30012
3. (An) A. Ancona - Théorie du potentiel sur les graphes et les variétés, Lecture Notes in Math.1427, p 3-112,1998. Zbl0719.60074
4. (Av) A. Avez - Théorème de Choquet-Deny pour les groupes à croissance non exponentielle, C.R.A.S.279, p 25-28, 1974. Zbl0292.60100MR353405
5. (Az) R. Azencott - Espaces de Poisson des groupes localement compacts, Lecture Notes in Math.148Springer, 1970. Zbl0208.15302MR501376
6. (B) Banach - Sur le problème de la mesure, Fund Math4, p 7-33, 1923. Zbl49.0145.03JFM49.0145.03
7. (Be-P) Benjamini- Pérès - Random walk on a tree and capacity in the interval, Ann. I.H.P., 1991. Zbl0767.60061
8. (Ba-L-P) P. Baldi, N. Lohoué, J. Peyrière - Sur la classification des groupes récurrents, C.R.A.S. t. 285, p 1103-1104, 1977. Zbl0376.60072MR518008
9. (Ba) M. Babillot - Théorie du renouvellement pour les chaînes semimarkoviennes transientes, Ann. I.H.P., vol. 24, n° 4, p 507-569, 1998. Zbl0681.60095MR978023
10. (Bo-L) P. Bougerol, J. Lacroix - Products of random matrices with applications to Schroëdinger operators, Progress in Probability and Statistics8, Birkhaüser, 1985. Zbl0572.60001MR886674
11. (Bi-R) Birgé, A. Raugi - Fonctions harmoniques sur les groupes moyennobles, C.R.A.S.278, p 1287-1289, 1974. Zbl0279.43006MR346918
12. (Bo) P. Bougerol - Comportement à l'infini du noyau potentiel du mouvement brownien sur un espace de Riemannien symétrique, Lecture Notes in Math.1096, p 90-115, 1983. Zbl0569.31009MR890355
13. (Br-D-P) A. Broise, F. Dal'bo, M. Peigné - Études spectrales d'opérateurs de transfert et applications, Astérisque238, 1998. Zbl0893.00017
14. (Bru-Re) A. Brunel, A. Revuz - Marches de Harris sur les groupes localement compacts, Ann. E.N.S., (4), 7, p 273-310, 1974. Zbl0324.60055MR365718
15. (C) Cartan - Théorie générale du balayage en potentiel newtonien, Ann. Univ. Grenoble Math. Phys.22, p 221-280, 1946. Zbl0061.22701MR20682
16. (Ca-L) R. Carmona, J. Lacroix - Spectral theory of random Schroëdinger operators, Probability and its applications Birkhaüser, 1990. Zbl0717.60074MR1102675
17. (Car) Cartwright - On the asymptotic behaviour of convolution powers of probabilities on discrete groups, Monatsh Math.107, p 287-290, 1989. Zbl0663.43001MR1012460
18. (Ch-D) G. Choquet, J. Deny - Sur l’équation de convolution $\mu =\mu *\sigma$, C.R.A.S. t. 250, p 799-801, 1960. Zbl0093.12802MR119041
19. (Co-S) T. Coulhon, L. Saloff- Coste -Isoperimetrie pour les groupes et les variétés, Rev. Mat. Iberoamericana9, p 293-314, 1993. Zbl0782.53066MR1232845
20. (Cr) P. Crépel - Récurrence des marches aléatoires sur les groupes de Lie, Lecture Notes in Math.532, p 50-69, Springer, 1973. Zbl0352.22009MR651920
21. (D) Deny - Méthodes hilbertiennes en théorie du potentiel, C.I.M.E.Rome ed. Cremonese, 1970. Zbl0212.13401
22. (Da) Damek - Pointwise estimates for the Poisson kernel on AN-groups by the Ancona method, Annales de la Faculté des Sciences de Toulouse, à paraître, 1998. Zbl0876.22008
23. (De) Y. Derriennic - Frontière de Martin pour les marches aléatoires sur le groupe libre, Z. Wahr32, p 261-276, 1975. Zbl0364.60117
24. (Di) Diaconis - Applications of non commutative Fourier analysis to probability problems, Lecture Notes in Math.1362, p 51-100, 1988. Zbl0662.60013
25. (Do-S) Doyle- Snell - Random walks and electrical networks, Carus Math. Monographs22, 1988. Zbl0583.60065
26. (Dy-M) E.B. Dynkin - M. Malyutov - Random walks on groups with a finite number of generators, Soviet Math. Dokl2, p 399-402, 1961. Zbl0214.44101
27. (Dy) E.B. Dynkin - Non negative eigenfunctions of the Laplace-Beltrami operator in certain symmetric spaces, Math. USSR Isvestyia72, p 203-226, 1968. Zbl0187.04202
28. (Eck) Eckmann - Lois de Kirchoff et fonctions discrètes harmoniques, Bull. Soc. Vaud Sc Nat63, n° 261, Lausanne, 1945. 
29. (El) L. Elie - Comportement asymptotique du noyau potentiel sur les groupes de Lie, Ann. E.N.S. t. 15, p 257-364, 1982. Zbl0509.60070MR683637
30. (F) Feller - An introduction to probability theory and its applications, vol. I, II, 3d ed., New York, 1968. Zbl0039.13201
31. (Fui) H. Furstenberg - A Poisson formula for semi-simple Lie groups, Annals of Math. 2, t. 77, p 335-386, 1963. Zbl0192.12704MR146298
32. (Fu2) H. Furstenberg - Non commuting random products, TAM.S108, p 377-428, 1963. Zbl0203.19102MR163345
33. (Fu3) H. Furstenberg - Random walk and discrete subgroups of Lie groups, Advances in Probability and related topics (Ed. P. Ney) vol. 1, p 1-63, M. Dekker, 1971. Zbl0221.22008MR284569
34. (Fu4) H. Furstenberg - Boundary, theory and stochastic processes on homogeneous space, Proc. Symp. Pure Math.36, p 193-229, 1972. Zbl0289.22011MR352328
35. (Go-G) I. Goldcheid - Y. Guivarc'h - Zariski closure and the dimension of the Gaussian law of the product of random matrices, Prob. theory related fields, 105, p 109-142, 1996. Zbl0854.60006MR1389734
36. (Go-M-P) I. Goldcheid, S.A. Molcanov, L.A. Pastur - A pure point spectrum of the one-dimensional Schroëdinger operators, Funct. Anal. Appl.11, p 1-10, 1977. Zbl0368.34015MR470515
37. (Go-M) I. Goldcheid, G.A. Margulis - Lyapunov indices of a product of random matrices, Russian Math. Surveys44-5, p 11-81, 1989. Zbl0705.60012MR1040268
38. (Gree) Greenleaf - Invariant means on topological groups, Van Nostrand, New York, 1969. 
39. (Gren) Grenander - Probabilities on algebraic structures, Wiley, 1963. Zbl0131.34804
40. (Gri) Grigortchuk - The growth degrees of finitely generated groups and the theory of invariant means, Math. USSR Izv25, p 259-300, 1985. Zbl0583.20023
41. (Gri-Dlh) Grigortchuk, De La Harpe - On problems related to growth, entropy and spectrum in group theory, Journal of dynamical and control systems3, n° 1, p 55-89, 1997. Zbl0949.20033MR1436550
42. (Gro) M. Gromov - Groups of polynomial growth and expanding maps, Publ. Math. I.H.E.S., n° 53, p 53-78, 1981. Zbl0474.20018MR623534
43. (Gu-H) Y. Guivarc'h, J. Hardy - Théorèmes limites pour une classe de chaînes de Markov et applications aux difféomorphismes d'Anosov, Ann. I.H.P.24, n° 1, p 73-98, 1988. Zbl0649.60041MR937957
44. (Gu-J-T) Y. Guivarc'h , Ji, J.C. Taylor - Compactifications of symmetric spaces, Progress in Math., Birkhaüser, 1998. Zbl1053.31006MR1633171
45. (Gu-K-R) Y. Guivarc'h, M. Keane, B. Roynette - Marches aléatoires sur les groupes de Lie, Lecture Notes in Math.624, Springer, 1977. Zbl0367.60081MR517359
46. (Gu-R1) Y. Guivarc'h, A. Raugi - Frontières de Furstenberg, propriétés de contraction et théorèmes de convergence, Z. Wahr89, p 187-242, 1985. Zbl0558.60009MR779457
47. (Gu-R2) Y. Guivarc'h, A. Raugi - Products of random matrices and convergence theorems, Contemraryt Math.50A.M.S., p 31-54, 1986. Zbl0592.60015MR841080
48. (Gu1) Y. Guivarc'h - Croissance polynomiale et périodes des fonctions harmoniques, Bull. S.M.F.101, p 333-379, 1973. Zbl0294.43003MR369608
49. (Gu2) Y. Guivarc'h - Une loi des grands nombres pour les groupes de Lie, Astérisque74, p 47-98, 1980. Zbl0448.60007MR588157
50. (Gu3) Y. Guivarc'h- Sur les exposants de Liapunoff des marches aléatoires, C.R.A.S.292, p 327-329, 1981. Zbl0482.60020MR608846
51. (Gu4) Y. Guivarc'h - Produits de matrices aléatoires et applications aux sousgroupes du groupe linéaire, Ergod. Th. and Dyn. Syst.10, p 483-512, 1990. Zbl0715.60008MR1074315
52. (Gu5) Y. Guivarc'h -Quelques propriétés asymptotiques des produits de matrices aléatoires, Lecture Notes in math.774, p 176-250, Springer, 1980. Zbl0433.60007MR590627
53. (Gu6) Y. Guivarc'h - Marches aléatoires sur les groupes et problèmes connexes, Publications des séminaires de l'université de Rennes, 1993. Zbl0941.60016MR1347696
54. (H) Hadamard - Sur le battage des cartes et ses relations avec la mécanique statistique, Oeuvres t. 4, p 2071-2077, Éditions du C.N.R.S., 1968. JFM57.0611.03
55. (He-S) Hebish, L. Saloff-Coste - Gaussian estimates for Markov chains and random walks on groups, à paraître. Zbl0776.60086
56. (K) Kac - Probability and related topics in physical sciences, Interscience publishers, 1959. Zbl0087.33003
57. (Ka-V) V.A. Kaimanovich, A. M. Vershik - Random walks on discrete groups : boundary and entropy, Annals of prob. vol. 11 n° 3, p 457-490, 1983. Zbl0641.60009MR704539
58. (Ka1) V. A. Kaimanovich - An entropy criterion for maximality of the boundary of random walks on discrete groups, Sov. Math. Dokl vol. 31, n° 1, p 193-197, 1985. Zbl0611.60060MR780288
59. (Ka2) V. A. Kaimanovich - Boundaries of invariant Markov operators : the identification problem, Lecture Note series of London Math. Soc.228, p 127-176, 1996. Zbl0848.60073MR1411218
60. (Kaw-I) Kawada- Ito - On the probability distribution on a compact group I, Proc. Phys. Math. Soc.Japan22, p 226-278, 1940. Zbl0026.13801MR3462JFM66.0544.04
61. (Ke1) H. Kesten - Symmetric random walks on groups, TAMS92, p 336-354, 1959. Zbl0092.33503MR109367
62. (Ke2) H. Kesten - The Martin boundary of recurrent random walks on countable groups, Proc. Th. Berkeley Symp. on Math. Statistics and Probability t. II , p 51-74, 1967. Zbl0234.60091MR214137
63. (Ke3) H. Kesten - Random difference equations and renewal theory for products of random matrices, Acta Math.131, p 208-248, 1973. Zbl0291.60029MR440724
64. (Ko) Koranyi - A survey of harmonic functions on symmetric spaces, Proceedings of Symposia in Pure Math.35, I, p 323-344, 1979. Zbl0433.43010MR545272
65. (L) Levy - Processus stochastiques et mouvement brownien, 2ème ed. Gauthier-Villars, Paris1965. Zbl0034.22603MR190953
66. (LeD) F. Le Drappier - Quelques propriétés des exposants caractéristiques, Lecture Notes in Math.1097, p 305-396, Springer, 1984. Zbl0578.60029MR876081
67. (LeP) E. Le Page - Théorèmes limites pour les produits de matrices aléatoires, Lecture Notes in math.928, p 258-303, Springer1982. Zbl0506.60019MR669072
68. (Let) Letchikov - Products of unimodular indépendant random matrices, Russian Math. Surveys51, n° 1, p 49-96, 1996. Zbl0871.15022MR1392671
69. (Li-P) Lin- Pinchover - Manifolds with Group Actions and Elliptic Operators, Memoirs A.M.S.112, n° 540, 1994. Zbl0816.58041MR1230774
70. (Lo) Losert - On the structure of groups with polynomial growth, Math. Zeit.196, p 109-117, 1987. Zbl0633.22002MR888132
71. (Lu-P-S) A. Lubotsky, R. Phillips, P. Sarnak - Hecke operators and distributing points on the sphere I, CPAM39, p 149-186, 1987. Zbl0619.10052MR861487
72. (Lu) Lubotsky - Discrete groups, expanding graphs and invariant measures, Progress in Math., Birkhaüser, 1994. Zbl0826.22012MR1308046
73. (Ly-S) T. Lyons, D. Sullivan - Function theory, random paths and covering spaces, Journal of Differential Geometry19, p 299-323, 1984. Zbl0554.58022MR755228
74. (Ly) T. Lyons - A simple criterion for transience of a reversible Markov chain, Ann. Prob.11, p 393-402, 1983. Zbl0509.60067MR690136
75. (Mi) Milnor - A note on curvature and fondamental group, J. Diff. Geometry2, p 447-450, 1968. Zbl0162.25401MR232311
76. (N-W) Nash- Williams - Random walks and electrical currents in networks, Proc. Cambridge Phil. Soc.55, p 181-194, 1959. Zbl0100.13602MR124932
77. (Ne) Nevo - Pointwise ergodic theorems for radial averages on simple Lie groups I, Duke Journal of Maths76, n° 1, p 113-140, 1994. Zbl0838.43013MR1301188
78. (O) Oseledets - A multiplicative ergodic theorem Lyapunov : characteristic exponents for dynamical systems, Trans. Moscow Math. Soc. (A.M.S.) 19, p 197-231, 1968. Zbl0236.93034MR240280
79. (P) Poincaré - Calcul des Probabilités, 2ème ed., Gauthier-Villars, Paris, 1912. JFM43.0308.04
80. (Pi) Pier - Amenable locally compact groups, WileyNew York, 1984. Zbl0621.43001MR767264
81. (Ra) A. Raugi - Fonctions harmoniques et théorèmes limites pour les marches aléatoires sur les groupes de Lie, Bull. S.M.F. mém.54, 1977. 
82. (Ro) J. Rosenblatt - Ergodicity and mixing of random walks on locally compact groups, Math. Ann.257, p 31-42, 1981. Zbl0451.60011MR630645
83. (Sa) Sarnak - Some applications of modular forms, Cambridge tracts in Math., 1990. Zbl1141.11023
84. (So) Soardi - Potential theory on infinite networks, SpringerLecture Notes1590, 1994. Zbl0818.31001MR1324344
85. (Sp) F. Spitzer - Principles of random walks, Van Nostrand, 1964. Zbl0175.16702MR171290
86. (Ts) Tsuji - Potential theory in modern function theory, Tokyo Maruzen, 1959. Zbl0087.28401MR114894
87. (Tu1) Tutubalin - Some theorems of the type of the strong law of large numbers, Theory of Proba and its applications14, p 313-319, 1969. Zbl0196.20904
88. (Tu2) Tutubalin - A central limit theorem for products of random matrices and some of its applications, Symposia Math. vol. 21, Academic Press, p 101-116, 1977. Zbl0375.60029MR478273
89. (V-S-C) N.TH. Varopoulos, L. Saloff-Coste, T. Coulhon - Analysis and Geometry on groups, Cambridge University Press, 1991. Zbl1179.22009MR1218884
90. (V1) N. TH. Varopoulos - Analysis on Lie groups, Rev. Math. Iberoamericana12, n° 3, p 791-917, 1996. Zbl0881.22009MR1435484
91. (V2) N. TH. Varopoulos - Information theory and harmonic functions, Bull Sc. Math.110, p 347-389, 1986. Zbl0646.31007MR884214
92. (V3) N. TH. Varopoulos - Théorie du potentiel sur les groupes et les variétés, CRAS sér. I302, p. 203-205, 1986. Zbl0605.31005MR832044
93. (Vi) Virtser - Central limit theorem for semi-simple Lie groups, Theory Proba Appl.15, p 667-687, 1990. Zbl0232.60004
94. (W) Weyl - The method of orthogonal projections in potential theory, Duke math. Journal7, p 411-444, 1940. MR3331JFM66.0444.01
95. (Wo) Woess - Random walks on infinite graphs and groups. A survey on selected topics, Bull. London Math. Soc.26, p 1-60, 1994. Zbl0830.60061MR1246471
96. (Zi) R. Zimmer - Ergocic theory and semi-simple groups, BirkhaüserBoston, 1984.