Random walks on a tree and capacity in the interval
Annales de l'I.H.P. Probabilités et statistiques, Tome 28 (1992) no. 4, pp. 557-592. 
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Benjamini, Itai; Peres, Yuval. Random walks on a tree and capacity in the interval. Annales de l'I.H.P. Probabilités et statistiques, Tome 28 (1992) no. 4, pp. 557-592. http://archive.numdam.org/item/AIHPB_1992__28_4_557_0/

[A] A. Ancona, Negatively Curved Manifolds, Elliptic Operators and the Martin Boundary, Ann. of Math., Vol. 125, 1987, pp. 495-536. | MR | Zbl

[C] L. Carleson, Selected Problems on Exceptional Sets, Van Nostrand, 1967. | MR | Zbl

[Ca] P. Cartier, Fonctions harmoniques sur un arbre, Symposia Math., Vol. 9, 1972, pp. 203-270. | MR | Zbl

[DS] P. Doyle and J.L. Snell, Random Walks and Electrical Networks, Carus Math. Monographs (1981). | Zbl

[Fr] O. Frostman, Potentiel d'équilibre et capacité des ensembles, Thesis, Lund, 1935. | JFM | Zbl

[Fu] H. Furstenberg, Intersections of Cantor Sets and Transverality of Semigroups, in Problems in Analysis, a symposium in honor of S. Bochner, R. C. GUNNING Ed., Princeton University press, 1970, pp. 41-59. | MR | Zbl

[G] E. Ghys, and P. De La Harpe, Sur les groupes hyperboliques d'après Mikhael Gromov, preprint.

[K] J.P. Kahane, Some Random Series of Functions, 2nd Ed., Cambridge University press, 1985. | MR | Zbl

[Kak] S. Kakutani, Two-dimensional Brownian Motion and Harmonic Functions, Proc. Imperial. Acad., Tokyo, Vol. 20, 1944, pp. 706-714. | MR | Zbl

[Ki] Y. Kifer, A Lower Bound for Hausdorff Dimension of Harmonic Measures on Negatively Curved Manifolds, preprint, 1989. | MR

[KL] Y. Kifer and F. Ledrappier, Hausdorff Dimension of Harmonic Measures on Negatively Curved Manifolds, preprint, 1988. | MR

[KSK] J.G. Kemeny, J.L. Snell and A.W. Knapp, Denumerable Markov Chains, 2nd Ed., Springer Verlag, 1976. | MR | Zbl

[L1] T. Lyons, Transience of Reversible Markov Chains, Ann. of Probability, Vol. 11, 2, 1983, pp. 393-402. | MR | Zbl

[L2] R. Lyons, Random Walks and Percolation on Trees, Ann. of Probability, Vol. 18, 3, 1990, pp. 931-958. | MR | Zbl

[M] G. Michon, Les Cantors reguliers, C. R. Acad. Sci. Paris, t. 30, Series I, 1987, pp. 673-675. | MR | Zbl

[N] C. Nash-Williams, Random Walks and Electric Currents in Networks, Proc. Camb. Phil. Soc., Vol. 55, 1959, pp. 181-194. | MR | Zbl

[Ta] S.J. Taylor, The Measure Theory of Random Fractals, Math. Proc. Camb. Phil. Soc., Vol. 100, 1986, pp. 383-406. | MR | Zbl

[Ts] M. Tsuji, Potential Theory in Modern Function Theory, Maruzen, Tokyo, 1959. | MR | Zbl

[W] J. Wermer, Potential Theory, Springer Lecture Notes in Mathematics, No. 408, Springer Verlag, 1974. | MR | Zbl