@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},
year = {1996-1997},
publisher = {D\'epartement de Math\'ematiques et Informatique, Universit\'e de Rennes},
number = {2},
language = {fr},
url = {https://www.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 - https://www.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 https://www.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, Fascicule de probabilités, no. 2 (1996-1997), article no. 3, 37 p.. https://www.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. | Zbl | MR
(Az) - Espaces de Poisson des groupes localement compacts, Lecture Notes in Math. 148 Springer, 1970. | Zbl | MR
(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. | Zbl | Numdam
(Ba-L-P) , , - Sur la classification des groupes récurrents, C.R.A.S. t. 285, p 1103-1104, 1977. | Zbl | MR
(Ba) - Théorie du renouvellement pour les chaînes semimarkoviennes transientes, Ann. I.H.P., vol. 24, n° 4, p 507-569, 1998. | Zbl | MR | Numdam
(Bo-L) , - Products of random matrices with applications to Schroëdinger operators, Progress in Probability and Statistics 8, Birkhaüser, 1985. | Zbl | MR
(Bi-R) , - Fonctions harmoniques sur les groupes moyennobles, C.R.A.S. 278, p 1287-1289, 1974. | Zbl | MR
(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. | Zbl | MR
(Br-D-P) , , - Études spectrales d'opérateurs de transfert et applications, Astérisque 238, 1998. | Zbl | Numdam
(Bru-Re) , - Marches de Harris sur les groupes localement compacts, Ann. E.N.S., (4), 7, p 273-310, 1974. | Zbl | MR | Numdam
(C) - Théorie générale du balayage en potentiel newtonien, Ann. Univ. Grenoble Math. Phys. 22, p 221-280, 1946. | Zbl | MR | Numdam
(Ca-L) , - Spectral theory of random Schroëdinger operators, Probability and its applications Birkhaüser, 1990. | Zbl | MR
(Car) - On the asymptotic behaviour of convolution powers of probabilities on discrete groups, Monatsh Math. 107, p 287-290, 1989. | Zbl | MR
(Ch-D) , - Sur l’équation de convolution , C.R.A.S. t. 250, p 799-801, 1960. | Zbl | MR
(Co-S) , - -Isoperimetrie pour les groupes et les variétés, Rev. Mat. Iberoamericana 9, p 293-314, 1993. | Zbl | MR
(Cr) - Récurrence des marches aléatoires sur les groupes de Lie, Lecture Notes in Math. 532, p 50-69, Springer, 1973. | Zbl | MR
(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. | Zbl | Numdam
(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. | Zbl | MR | Numdam
(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. | Zbl | MR
(Fu2) - Non commuting random products, TAM.S 108, p 377-428, 1963. | Zbl | MR
(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. | Zbl | MR
(Fu4) - Boundary, theory and stochastic processes on homogeneous space, Proc. Symp. Pure Math. 36, p 193-229, 1972. | Zbl | MR
(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. | Zbl | MR
(Go-M-P) , , - A pure point spectrum of the one-dimensional Schroëdinger operators, Funct. Anal. Appl. 11, p 1-10, 1977. | Zbl | MR
(Go-M) , - Lyapunov indices of a product of random matrices, Russian Math. Surveys 44-5, p 11-81, 1989. | Zbl | MR
(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. | Zbl | MR
(Gro) - Groups of polynomial growth and expanding maps, Publ. Math. I.H.E.S., n° 53, p 53-78, 1981. | Zbl | MR | Numdam
(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. | Zbl | MR | Numdam
(Gu-J-T) , , - Compactifications of symmetric spaces, Progress in Math., Birkhaüser, 1998. | Zbl | MR
(Gu-K-R) , , - Marches aléatoires sur les groupes de Lie, Lecture Notes in Math. 624, Springer, 1977. | Zbl | MR
(Gu-R1) , - Frontières de Furstenberg, propriétés de contraction et théorèmes de convergence, Z. Wahr 89, p 187-242, 1985. | Zbl | MR
(Gu-R2) , - Products of random matrices and convergence theorems, Contemraryt Math. 50 A.M.S., p 31-54, 1986. | Zbl | MR
(Gu1) - Croissance polynomiale et périodes des fonctions harmoniques, Bull. S.M.F. 101, p 333-379, 1973. | Zbl | MR | Numdam
(Gu2) - Une loi des grands nombres pour les groupes de Lie, Astérisque 74, p 47-98, 1980. | Zbl | MR | Numdam
(Gu3) - Sur les exposants de Liapunoff des marches aléatoires, C.R.A.S. 292, p 327-329, 1981. | Zbl | MR
(Gu4) - Produits de matrices aléatoires et applications aux sousgroupes du groupe linéaire, Ergod. Th. and Dyn. Syst. 10, p 483-512, 1990. | Zbl | MR
(Gu5) -Quelques propriétés asymptotiques des produits de matrices aléatoires, Lecture Notes in math. 774, p 176-250, Springer, 1980. | Zbl | MR
(Gu6) - Marches aléatoires sur les groupes et problèmes connexes, Publications des séminaires de l'université de Rennes, 1993. | Zbl | MR
(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. | Zbl | MR
(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. | Zbl | MR
(Ka2) - Boundaries of invariant Markov operators : the identification problem, Lecture Note series of London Math. Soc. 228, p 127-176, 1996. | Zbl | MR
(Kaw-I) - - On the probability distribution on a compact group I, Proc. Phys. Math. Soc. Japan 22, p 226-278, 1940. | Zbl | MR | JFM
(Ke1) - Symmetric random walks on groups, TAMS 92, p 336-354, 1959. | Zbl | MR
(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. | Zbl | MR
(Ke3) - Random difference equations and renewal theory for products of random matrices, Acta Math. 131, p 208-248, 1973. | Zbl | MR
(Ko) - A survey of harmonic functions on symmetric spaces, Proceedings of Symposia in Pure Math. 35, I, p 323-344, 1979. | Zbl | MR
(L) - Processus stochastiques et mouvement brownien, 2ème ed. Gauthier-Villars, Paris 1965. | Zbl | MR
(LeD) - Quelques propriétés des exposants caractéristiques, Lecture Notes in Math. 1097, p 305-396, Springer, 1984. | Zbl | MR
(LeP) - Théorèmes limites pour les produits de matrices aléatoires, Lecture Notes in math. 928, p 258-303, Springer 1982. | Zbl | MR
(Let) - Products of unimodular indépendant random matrices, Russian Math. Surveys 51, n° 1, p 49-96, 1996. | Zbl | MR
(Li-P) - - Manifolds with Group Actions and Elliptic Operators, Memoirs A.M.S. 112, n° 540, 1994. | Zbl | MR
(Lo) - On the structure of groups with polynomial growth, Math. Zeit. 196, p 109-117, 1987. | Zbl | MR
(Lu-P-S) , , - Hecke operators and distributing points on the sphere I, CPAM 39, p 149-186, 1987. | Zbl | MR
(Lu) - Discrete groups, expanding graphs and invariant measures, Progress in Math., Birkhaüser, 1994. | Zbl | MR
(Ly-S) , - Function theory, random paths and covering spaces, Journal of Differential Geometry 19, p 299-323, 1984. | Zbl | MR
(Ly) - A simple criterion for transience of a reversible Markov chain, Ann. Prob. 11, p 393-402, 1983. | Zbl | MR
(Mi) - A note on curvature and fondamental group, J. Diff. Geometry 2, p 447-450, 1968. | Zbl | MR
(N-W) - - Random walks and electrical currents in networks, Proc. Cambridge Phil. Soc. 55, p 181-194, 1959. | Zbl | MR
(Ne) - Pointwise ergodic theorems for radial averages on simple Lie groups I, Duke Journal of Maths 76, n° 1, p 113-140, 1994. | Zbl | MR
(O) - A multiplicative ergodic theorem Lyapunov : characteristic exponents for dynamical systems, Trans. Moscow Math. Soc. (A.M.S.) 19, p 197-231, 1968. | Zbl | MR
(P) - Calcul des Probabilités, 2ème ed., Gauthier-Villars, Paris, 1912. | JFM
(Pi) - Amenable locally compact groups, Wiley New York, 1984. | Zbl | MR
(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. | Zbl | MR
(Sa) - Some applications of modular forms, Cambridge tracts in Math., 1990. | Zbl
(So) - Potential theory on infinite networks, Springer Lecture Notes 1590, 1994. | Zbl | MR
(Sp) - Principles of random walks, Van Nostrand, 1964. | Zbl | MR
(Ts) - Potential theory in modern function theory, Tokyo Maruzen, 1959. | Zbl | MR
(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. | Zbl | MR
(V-S-C) , , - Analysis and Geometry on groups, Cambridge University Press, 1991. | Zbl | MR
(V1) - Analysis on Lie groups, Rev. Math. Iberoamericana 12, n° 3, p 791-917, 1996. | Zbl | MR
(V2) - Information theory and harmonic functions, Bull Sc. Math. 110, p 347-389, 1986. | Zbl | MR
(V3) - Théorie du potentiel sur les groupes et les variétés, CRAS sér. I 302, p. 203-205, 1986. | Zbl | MR
(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. | MR | JFM
(Wo) - Random walks on infinite graphs and groups. A survey on selected topics, Bull. London Math. Soc. 26, p 1-60, 1994. | Zbl | MR
(Zi) - Ergocic theory and semi-simple groups, Birkhaüser Boston, 1984.






