Random walks on a tree and capacity in the interval
Annales de l'I.H.P. Probabilités et statistiques (1992)
- Volume: 28, Issue: 4, page 557-592
- ISSN: 0246-0203
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topBenjamini, Itai, and Peres, Yuval. "Random walks on a tree and capacity in the interval." Annales de l'I.H.P. Probabilités et statistiques 28.4 (1992): 557-592. <http://eudml.org/doc/77445>.
@article{Benjamini1992,
author = {Benjamini, Itai, Peres, Yuval},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {geometric criterion for transience of a random walk; logarithmic energy; harmonic measures; Diophantine approximation condition},
language = {eng},
number = {4},
pages = {557-592},
publisher = {Gauthier-Villars},
title = {Random walks on a tree and capacity in the interval},
url = {http://eudml.org/doc/77445},
volume = {28},
year = {1992},
}
TY - JOUR
AU - Benjamini, Itai
AU - Peres, Yuval
TI - Random walks on a tree and capacity in the interval
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1992
PB - Gauthier-Villars
VL - 28
IS - 4
SP - 557
EP - 592
LA - eng
KW - geometric criterion for transience of a random walk; logarithmic energy; harmonic measures; Diophantine approximation condition
UR - http://eudml.org/doc/77445
ER -
References
top- [A] A. Ancona, Negatively Curved Manifolds, Elliptic Operators and the Martin Boundary, Ann. of Math., Vol. 125, 1987, pp. 495-536. Zbl0652.31008MR890161
- [C] L. Carleson, Selected Problems on Exceptional Sets, Van Nostrand, 1967. Zbl0189.10903MR225986
- [Ca] P. Cartier, Fonctions harmoniques sur un arbre, Symposia Math., Vol. 9, 1972, pp. 203-270. Zbl0283.31005MR353467
- [DS] P. Doyle and J.L. Snell, Random Walks and Electrical Networks, Carus Math. Monographs (1981). Zbl0583.60065
- [Fr] O. Frostman, Potentiel d'équilibre et capacité des ensembles, Thesis, Lund, 1935. Zbl0013.06302JFM61.1262.02
- [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. Zbl0208.32203MR354562
- [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. Zbl0571.60002MR833073
- [Kak] S. Kakutani, Two-dimensional Brownian Motion and Harmonic Functions, Proc. Imperial. Acad., Tokyo, Vol. 20, 1944, pp. 706-714. Zbl0063.03107MR14647
- [Ki] Y. Kifer, A Lower Bound for Hausdorff Dimension of Harmonic Measures on Negatively Curved Manifolds, preprint, 1989. MR1088826
- [KL] Y. Kifer and F. Ledrappier, Hausdorff Dimension of Harmonic Measures on Negatively Curved Manifolds, preprint, 1988. MR951889
- [KSK] J.G. Kemeny, J.L. Snell and A.W. Knapp, Denumerable Markov Chains, 2nd Ed., Springer Verlag, 1976. Zbl0348.60090MR407981
- [L1] T. Lyons, Transience of Reversible Markov Chains, Ann. of Probability, Vol. 11, 2, 1983, pp. 393-402. Zbl0509.60067MR690136
- [L2] R. Lyons, Random Walks and Percolation on Trees, Ann. of Probability, Vol. 18, 3, 1990, pp. 931-958. Zbl0714.60089MR1062053
- [M] G. Michon, Les Cantors reguliers, C. R. Acad. Sci. Paris, t. 30, Series I, 1987, pp. 673-675. Zbl0582.54019MR802649
- [N] C. Nash-Williams, Random Walks and Electric Currents in Networks, Proc. Camb. Phil. Soc., Vol. 55, 1959, pp. 181-194. Zbl0100.13602MR124932
- [Ta] S.J. Taylor, The Measure Theory of Random Fractals, Math. Proc. Camb. Phil. Soc., Vol. 100, 1986, pp. 383-406. Zbl0622.60021MR857718
- [Ts] M. Tsuji, Potential Theory in Modern Function Theory, Maruzen, Tokyo, 1959. Zbl0087.28401MR114894
- [W] J. Wermer, Potential Theory, Springer Lecture Notes in Mathematics, No. 408, Springer Verlag, 1974. Zbl0297.31001MR454033
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