Existence of positive harmonic functions on groups and on covering manifolds
Annales de l'I.H.P. Probabilités et statistiques, Tome 31 (1995) no. 1, pp. 59-80.
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     title = {Existence of positive harmonic functions on groups and on covering manifolds},
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     number = {1},
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     url = {http://www.numdam.org/item/AIHPB_1995__31_1_59_0/}
}
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Bougerol, Philippe; Elie, Laure. Existence of positive harmonic functions on groups and on covering manifolds. Annales de l'I.H.P. Probabilités et statistiques, Tome 31 (1995) no. 1, pp. 59-80. http://www.numdam.org/item/AIHPB_1995__31_1_59_0/

[1] G. Alexopoulos, Fonctions harmoniques bornées sur les groupes résolubles, C. R. Acad. Sci. Paris, I, Vol. 305, 1987, pp. 777-779. | MR | Zbl

[2] A. Ancona, Théorie du potentiel sur les graphes et les variétés, Lecture Notes in Math., Vol. 1427, 1990, Springer Verlag, Berlin, Heidelberg, New York, pp. 4-112. | MR | Zbl

[3] S. Asmussen, Applied probability and queues, Wiley, New York, 1987. | MR | Zbl

[4] A. Avez, Harmonic functions on groups, in Differential geometry and relativity, Reidel, Dordrecht, 1976, pp. 27-32. | MR | Zbl

[5] R. Azencott, Espaces de Poisson des groupes localement compacts, Lecture Notes in Math., Vol. 148, 1970, Springer Verlag, Berlin, Heidelberg, New York. | MR | Zbl

[6] M. Babillot, Ph. Bougerol and L. Elie, in preparation.

[7] W. Ballmann and F. Ledrappier, Discretization of positive harmonic functions on Riemannian manifolds and Martin boundaries, Actes de la Table Ronde de Géométrie Différentielle en l'honneur de Marcel Berger, Arthur L. Besse, Ed., Séminaires et Congrès 1, 1994, SMF. | Zbl

[8] N. Bourbaki, Lie groups and Lie algebra, Hermann, Paris, 1975.

[9] R. Brooks, The fundamental group and the spectrum of the Laplacian, Comm. Math. Helv., Vol. 56, 1981, pp. 501-508. | MR | Zbl

[10] E. Cinlar, Markov renewal theory, Adv. Appl. Prob., Vol. 1, 1969, pp. 123-187. | MR | Zbl

[11] L. Elie, Comportement asymptotique du noyau potentiel sur les groupes de Lie, Ann. Scient. Ec. Norm. Sup., Vol. 15, 1982, pp. 257-364. | Numdam | MR | Zbl

[12] W. Feller, An introduction to probability and its application, Vol. 2, 1971, Wiley, New York. | MR

[13] Y. Guivarc'H, Croissance polynomiale et périodes des fonctions harmoniques, Bull. Soc. Math. France, Vol. 101, 1973, pp. 178-250. | Numdam | MR | Zbl

[14] Y. Guivarc'H, Sur la loi des grands nombres et le rayon spectral d'une marche aléatoire, Astérisque, Vol. 74, 1980, pp. 47-98. | Numdam | MR | Zbl

[15] Y. Guivarc'H, Application d'un théorème limite local à la transience et à la récurrence de marches de Markov, in Théorie du potentiel, Proceedings, Lecture Notes in Math., Vol. 1096, 1984, Springer Verlag, Berlin, Heidelberg, New York, pp. 301-332. | MR | Zbl

[16] Y. Guivarc'H, M. Keane and B. Roynette, Marches aléatoires sur les groupes de Lie, Lecture Notes in Math., Vol. 624, 1977, Springer Verlag, Berlin, Heidelberg, New York. | MR | Zbl

[17] A. Gut, Stopped random walks, Springer Verlag, Berlin, Heidelberg, New York, 1988. | MR | Zbl

[18] W. Hebish, L. Saloff Coste, Gaussian estimate for Markov chains and random walks on groups, Ann. Probab., Vol. 21, 1993, pp. 673-709. | MR | Zbl

[19] J. Jacod, Théorème de renouvellement et classification pour les chaînes semi-markoviennes, Ann. Inst. H. Poincaré, Vol. 7, 1971, pp. 83-129. | Numdam | MR | Zbl

[20] V.A. Kaimanovitch, Boundaries of random walks on polycyclic groups and the law of large numbers for solvable Lie groups, Vestnik Leningrad University: Mathematics, Vol. 20, 1987, pp. 49-52. | Zbl

[21] V.A. Kaimanovitch, Discretization of bounded harmonic functions on Riemannian manifolds and entropy, in Proceedings of the International Conference on Potential Theory, Nagoya, (M. Kishi, Ed.), de Gruyter, Berlin, 1992, pp. 213-223. | MR | Zbl

[22] M. Lin, Conservative Markov processes on a topological space, Israel J. Math., Vol. 8, 1970, pp. 165-186. | MR | Zbl

[23] V. Losert, On the structure of groups with polynomial growth, Math. Z., Vol. 195, 1987, pp. 109-117. | MR | Zbl

[24] T. Lyons, D. Sullivan, Function theory, random paths and covering spaces, J. Diff. Geom., Vol. 19, 1984, pp. 299-323. | MR | Zbl

[25] J. Milnor, A note on curvature and the fundamental group, J. Diff. Geom., Vol. 2, 1968, pp. 1-7. | MR | Zbl

[26] S.A. Molchanov, Martin boundaries for invariant Markov processes on a solvable group, Theory Probab. Appl., Vol. 12, 1967, pp. 310-314. | Zbl

[27] D. Montgomery and L. Zippin, Topological transformations groups, Interscience Publishers, New York, 1955. | MR | Zbl