@article{PSMIR_1996-1997___2_A3_0, author = {Guivarc'h, Yves}, title = {Marches al\'eatoires sur les groupes}, journal = {Publications de l'Institut de recherche math\'ematiques de Rennes}, eid = {3}, pages = {1--37}, publisher = {D\'epartement de Math\'ematiques et Informatique, Universit\'e de Rennes}, number = {2}, year = {1996-1997}, language = {fr}, url = {http://archive.numdam.org/item/PSMIR_1996-1997___2_A3_0/} }
TY - JOUR AU - Guivarc'h, Yves TI - Marches aléatoires sur les groupes JO - Publications de l'Institut de recherche mathématiques de Rennes PY - 1996-1997 SP - 1 EP - 37 IS - 2 PB - Département de Mathématiques et Informatique, Université de Rennes UR - http://archive.numdam.org/item/PSMIR_1996-1997___2_A3_0/ LA - fr ID - PSMIR_1996-1997___2_A3_0 ER -
%0 Journal Article %A Guivarc'h, Yves %T Marches aléatoires sur les groupes %J Publications de l'Institut de recherche mathématiques de Rennes %D 1996-1997 %P 1-37 %N 2 %I Département de Mathématiques et Informatique, Université de Rennes %U http://archive.numdam.org/item/PSMIR_1996-1997___2_A3_0/ %G fr %F PSMIR_1996-1997___2_A3_0
Guivarc'h, Yves. Marches aléatoires sur les groupes. Publications de l'Institut de recherche mathématiques de Rennes, no. 2 (1996-1997), article no. 3, 37 p. http://archive.numdam.org/item/PSMIR_1996-1997___2_A3_0/
[A-K] Uniform distribution of points on a sphere and some ergodic properties of solutions of differential equations in a complex region, Sov. Math Dokl 4 n° 1, p 1-5, 1963. | Zbl
, -(Ah) Conformal invariants. Topics in geometric function theory, Mac Graw Hill, New York, 1973. | Zbl
-(An) Théorie du potentiel sur les graphes et les variétés, Lecture Notes in Math. 1427, p 3-112,1998. | Zbl
-(Av) Théorème de Choquet-Deny pour les groupes à croissance non exponentielle, C.R.A.S. 279, p 25-28, 1974. | MR | Zbl
-(Az) Espaces de Poisson des groupes localement compacts, Lecture Notes in Math. 148 Springer, 1970. | MR | Zbl
-(B) Sur le problème de la mesure, Fund Math 4, p 7-33, 1923. | JFM
-(Be-P) Random walk on a tree and capacity in the interval, Ann. I.H.P., 1991. | Numdam | Zbl
- -(Ba-L-P) Sur la classification des groupes récurrents, C.R.A.S. t. 285, p 1103-1104, 1977. | MR | Zbl
, , -(Ba) Théorie du renouvellement pour les chaînes semimarkoviennes transientes, Ann. I.H.P., vol. 24, n° 4, p 507-569, 1998. | Numdam | MR | Zbl
-(Bo-L) Products of random matrices with applications to Schroëdinger operators, Progress in Probability and Statistics 8, Birkhaüser, 1985. | MR | Zbl
, -(Bi-R) Fonctions harmoniques sur les groupes moyennobles, C.R.A.S. 278, p 1287-1289, 1974. | MR | Zbl
, -(Bo) 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. | MR | Zbl
-(Br-D-P) Études spectrales d'opérateurs de transfert et applications, Astérisque 238, 1998. | Numdam | Zbl
, , -(Bru-Re) Marches de Harris sur les groupes localement compacts, Ann. E.N.S., (4), 7, p 273-310, 1974. | Numdam | MR | Zbl
, -(C) Théorie générale du balayage en potentiel newtonien, Ann. Univ. Grenoble Math. Phys. 22, p 221-280, 1946. | Numdam | MR | Zbl
-(Ca-L) Spectral theory of random Schroëdinger operators, Probability and its applications Birkhaüser, 1990. | MR | Zbl
, -(Car) On the asymptotic behaviour of convolution powers of probabilities on discrete groups, Monatsh Math. 107, p 287-290, 1989. | MR | Zbl
-(Ch-D) Sur l’équation de convolution , C.R.A.S. t. 250, p 799-801, 1960. | MR | Zbl
, -(Co-S) Isoperimetrie pour les groupes et les variétés, Rev. Mat. Iberoamericana 9, p 293-314, 1993. | MR | Zbl
, - -(Cr) Récurrence des marches aléatoires sur les groupes de Lie, Lecture Notes in Math. 532, p 50-69, Springer, 1973. | MR | Zbl
-(D) Méthodes hilbertiennes en théorie du potentiel, C.I.M.E. Rome ed. Cremonese, 1970. | Zbl
-(Da) Pointwise estimates for the Poisson kernel on AN-groups by the Ancona method, Annales de la Faculté des Sciences de Toulouse, à paraître, 1998. | Numdam | Zbl
-(De) Frontière de Martin pour les marches aléatoires sur le groupe libre, Z. Wahr 32, p 261-276, 1975. | Zbl
-(Di) Applications of non commutative Fourier analysis to probability problems, Lecture Notes in Math. 1362, p 51-100, 1988. | Zbl
-(Do-S) Random walks and electrical networks, Carus Math. Monographs 22, 1988. | Zbl
- -(Dy-M) Random walks on groups with a finite number of generators, Soviet Math. Dokl 2, p 399-402, 1961. | Zbl
- -(Dy) Non negative eigenfunctions of the Laplace-Beltrami operator in certain symmetric spaces, Math. USSR Isvestyia 72, p 203-226, 1968. | Zbl
-(Eck) Lois de Kirchoff et fonctions discrètes harmoniques, Bull. Soc. Vaud Sc Nat 63, n° 261, Lausanne, 1945.
-(El) Comportement asymptotique du noyau potentiel sur les groupes de Lie, Ann. E.N.S. t. 15, p 257-364, 1982. | Numdam | MR | Zbl
-(F) An introduction to probability theory and its applications, vol. I, II, 3d ed., New York, 1968. | Zbl
-(Fui) A Poisson formula for semi-simple Lie groups, Annals of Math. 2, t. 77, p 335-386, 1963. | MR | Zbl
-(Fu2) Non commuting random products, TAM.S 108, p 377-428, 1963. | MR | Zbl
-(Fu3) 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. | MR | Zbl
-(Fu4) Boundary, theory and stochastic processes on homogeneous space, Proc. Symp. Pure Math. 36, p 193-229, 1972. | MR | Zbl
-(Go-G) Zariski closure and the dimension of the Gaussian law of the product of random matrices, Prob. theory related fields, 105, p 109-142, 1996. | MR | Zbl
- -(Go-M-P) A pure point spectrum of the one-dimensional Schroëdinger operators, Funct. Anal. Appl. 11, p 1-10, 1977. | MR | Zbl
, , -(Go-M) Lyapunov indices of a product of random matrices, Russian Math. Surveys 44-5, p 11-81, 1989. | MR | Zbl
, -(Gree) Invariant means on topological groups, Van Nostrand, New York, 1969.
-(Gren) Probabilities on algebraic structures, Wiley, 1963. | Zbl
-(Gri) The growth degrees of finitely generated groups and the theory of invariant means, Math. USSR Izv 25, p 259-300, 1985. | Zbl
-(Gri-Dlh) On problems related to growth, entropy and spectrum in group theory, Journal of dynamical and control systems 3, n° 1, p 55-89, 1997. | MR | Zbl
, -(Gro) Groups of polynomial growth and expanding maps, Publ. Math. I.H.E.S., n° 53, p 53-78, 1981. | Numdam | MR | Zbl
-(Gu-H) 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. | Numdam | MR | Zbl
, -(Gu-J-T) Compactifications of symmetric spaces, Progress in Math., Birkhaüser, 1998. | MR | Zbl
, , -(Gu-K-R) Marches aléatoires sur les groupes de Lie, Lecture Notes in Math. 624, Springer, 1977. | MR | Zbl
, , -(Gu-R1) Frontières de Furstenberg, propriétés de contraction et théorèmes de convergence, Z. Wahr 89, p 187-242, 1985. | MR | Zbl
, -(Gu-R2) Products of random matrices and convergence theorems, Contemraryt Math. 50 A.M.S., p 31-54, 1986. | MR | Zbl
, -(Gu1) Croissance polynomiale et périodes des fonctions harmoniques, Bull. S.M.F. 101, p 333-379, 1973. | Numdam | MR | Zbl
-(Gu2) Une loi des grands nombres pour les groupes de Lie, Astérisque 74, p 47-98, 1980. | Numdam | MR | Zbl
-(Gu3) Sur les exposants de Liapunoff des marches aléatoires, C.R.A.S. 292, p 327-329, 1981. | MR | Zbl
-(Gu4) Produits de matrices aléatoires et applications aux sousgroupes du groupe linéaire, Ergod. Th. and Dyn. Syst. 10, p 483-512, 1990. | MR | Zbl
-(Gu5) Quelques propriétés asymptotiques des produits de matrices aléatoires, Lecture Notes in math. 774, p 176-250, Springer, 1980. | MR | Zbl
-(Gu6) Marches aléatoires sur les groupes et problèmes connexes, Publications des séminaires de l'université de Rennes, 1993. | MR | Zbl
-(H) 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. | JFM
-(He-S) Gaussian estimates for Markov chains and random walks on groups, à paraître. | Zbl
, -(K) Probability and related topics in physical sciences, Interscience publishers, 1959. | Zbl
-(Ka-V) Random walks on discrete groups : boundary and entropy, Annals of prob. vol. 11 n° 3, p 457-490, 1983. | MR | Zbl
, -(Ka1) 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. | MR | Zbl
-(Ka2) Boundaries of invariant Markov operators : the identification problem, Lecture Note series of London Math. Soc. 228, p 127-176, 1996. | MR | Zbl
-(Kaw-I) On the probability distribution on a compact group I, Proc. Phys. Math. Soc. Japan 22, p 226-278, 1940. | JFM | MR | Zbl
- -(Ke1) Symmetric random walks on groups, TAMS 92, p 336-354, 1959. | MR | Zbl
-(Ke2) 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. | MR | Zbl
-(Ke3) Random difference equations and renewal theory for products of random matrices, Acta Math. 131, p 208-248, 1973. | MR | Zbl
-(Ko) A survey of harmonic functions on symmetric spaces, Proceedings of Symposia in Pure Math. 35, I, p 323-344, 1979. | MR | Zbl
-(L) Processus stochastiques et mouvement brownien, 2ème ed. Gauthier-Villars, Paris 1965. | MR | Zbl
-(LeD) Quelques propriétés des exposants caractéristiques, Lecture Notes in Math. 1097, p 305-396, Springer, 1984. | MR | Zbl
-(LeP) Théorèmes limites pour les produits de matrices aléatoires, Lecture Notes in math. 928, p 258-303, Springer 1982. | MR | Zbl
-(Let) Products of unimodular indépendant random matrices, Russian Math. Surveys 51, n° 1, p 49-96, 1996. | MR | Zbl
-(Li-P) Manifolds with Group Actions and Elliptic Operators, Memoirs A.M.S. 112, n° 540, 1994. | MR | Zbl
- -(Lo) On the structure of groups with polynomial growth, Math. Zeit. 196, p 109-117, 1987. | MR | Zbl
-(Lu-P-S) Hecke operators and distributing points on the sphere I, CPAM 39, p 149-186, 1987. | MR | Zbl
, , -(Lu) Discrete groups, expanding graphs and invariant measures, Progress in Math., Birkhaüser, 1994. | MR | Zbl
-(Ly-S) Function theory, random paths and covering spaces, Journal of Differential Geometry 19, p 299-323, 1984. | MR | Zbl
, -(Ly) A simple criterion for transience of a reversible Markov chain, Ann. Prob. 11, p 393-402, 1983. | MR | Zbl
-(Mi) A note on curvature and fondamental group, J. Diff. Geometry 2, p 447-450, 1968. | MR | Zbl
-(N-W) Random walks and electrical currents in networks, Proc. Cambridge Phil. Soc. 55, p 181-194, 1959. | MR | Zbl
- -(Ne) Pointwise ergodic theorems for radial averages on simple Lie groups I, Duke Journal of Maths 76, n° 1, p 113-140, 1994. | MR | Zbl
-(O) A multiplicative ergodic theorem Lyapunov : characteristic exponents for dynamical systems, Trans. Moscow Math. Soc. (A.M.S.) 19, p 197-231, 1968. | MR | Zbl
-(P) Calcul des Probabilités, 2ème ed., Gauthier-Villars, Paris, 1912. | JFM
-(Pi) Amenable locally compact groups, Wiley New York, 1984. | MR | Zbl
-(Ra) Fonctions harmoniques et théorèmes limites pour les marches aléatoires sur les groupes de Lie, Bull. S.M.F. mém. 54, 1977.
-(Ro) Ergodicity and mixing of random walks on locally compact groups, Math. Ann. 257, p 31-42, 1981. | MR | Zbl
-(Sa) Some applications of modular forms, Cambridge tracts in Math., 1990. | Zbl
-(So) Potential theory on infinite networks, Springer Lecture Notes 1590, 1994. | MR | Zbl
-(Sp) Principles of random walks, Van Nostrand, 1964. | MR | Zbl
-(Ts) Potential theory in modern function theory, Tokyo Maruzen, 1959. | MR | Zbl
-(Tu1) Some theorems of the type of the strong law of large numbers, Theory of Proba and its applications 14, p 313-319, 1969. | Zbl
-(Tu2) A central limit theorem for products of random matrices and some of its applications, Symposia Math. vol. 21, Academic Press, p 101-116, 1977. | MR | Zbl
-(V-S-C) Analysis and Geometry on groups, Cambridge University Press, 1991. | MR | Zbl
, , -(V1) Analysis on Lie groups, Rev. Math. Iberoamericana 12, n° 3, p 791-917, 1996. | MR | Zbl
-(V2) Information theory and harmonic functions, Bull Sc. Math. 110, p 347-389, 1986. | MR | Zbl
-(V3) Théorie du potentiel sur les groupes et les variétés, CRAS sér. I 302, p. 203-205, 1986. | MR | Zbl
-(Vi) Central limit theorem for semi-simple Lie groups, Theory Proba Appl. 15, p 667-687, 1990. | Zbl
-(W) The method of orthogonal projections in potential theory, Duke math. Journal 7, p 411-444, 1940. | JFM | MR
-(Wo) Random walks on infinite graphs and groups. A survey on selected topics, Bull. London Math. Soc. 26, p 1-60, 1994. | MR | Zbl
-(Zi) Ergocic theory and semi-simple groups, Birkhaüser Boston, 1984.
-