Random walks on a tree and capacity in the interval

Itai Benjamini; Yuval Peres

Annales de l'I.H.P. Probabilités et statistiques (1992)

  • Volume: 28, Issue: 4, page 557-592
  • ISSN: 0246-0203

How to cite

top

Benjamini, 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
  1. [A] A. Ancona, Negatively Curved Manifolds, Elliptic Operators and the Martin Boundary, Ann. of Math., Vol. 125, 1987, pp. 495-536. Zbl0652.31008MR890161
  2. [C] L. Carleson, Selected Problems on Exceptional Sets, Van Nostrand, 1967. Zbl0189.10903MR225986
  3. [Ca] P. Cartier, Fonctions harmoniques sur un arbre, Symposia Math., Vol. 9, 1972, pp. 203-270. Zbl0283.31005MR353467
  4. [DS] P. Doyle and J.L. Snell, Random Walks and Electrical Networks, Carus Math. Monographs (1981). Zbl0583.60065
  5. [Fr] O. Frostman, Potentiel d'équilibre et capacité des ensembles, Thesis, Lund, 1935. Zbl0013.06302JFM61.1262.02
  6. [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
  7. [G] E. Ghys, and P. De La Harpe, Sur les groupes hyperboliques d'après Mikhael Gromov, preprint. 
  8. [K] J.P. Kahane, Some Random Series of Functions, 2nd Ed., Cambridge University press, 1985. Zbl0571.60002MR833073
  9. [Kak] S. Kakutani, Two-dimensional Brownian Motion and Harmonic Functions, Proc. Imperial. Acad., Tokyo, Vol. 20, 1944, pp. 706-714. Zbl0063.03107MR14647
  10. [Ki] Y. Kifer, A Lower Bound for Hausdorff Dimension of Harmonic Measures on Negatively Curved Manifolds, preprint, 1989. MR1088826
  11. [KL] Y. Kifer and F. Ledrappier, Hausdorff Dimension of Harmonic Measures on Negatively Curved Manifolds, preprint, 1988. MR951889
  12. [KSK] J.G. Kemeny, J.L. Snell and A.W. Knapp, Denumerable Markov Chains, 2nd Ed., Springer Verlag, 1976. Zbl0348.60090MR407981
  13. [L1] T. Lyons, Transience of Reversible Markov Chains, Ann. of Probability, Vol. 11, 2, 1983, pp. 393-402. Zbl0509.60067MR690136
  14. [L2] R. Lyons, Random Walks and Percolation on Trees, Ann. of Probability, Vol. 18, 3, 1990, pp. 931-958. Zbl0714.60089MR1062053
  15. [M] G. Michon, Les Cantors reguliers, C. R. Acad. Sci. Paris, t. 30, Series I, 1987, pp. 673-675. Zbl0582.54019MR802649
  16. [N] C. Nash-Williams, Random Walks and Electric Currents in Networks, Proc. Camb. Phil. Soc., Vol. 55, 1959, pp. 181-194. Zbl0100.13602MR124932
  17. [Ta] S.J. Taylor, The Measure Theory of Random Fractals, Math. Proc. Camb. Phil. Soc., Vol. 100, 1986, pp. 383-406. Zbl0622.60021MR857718
  18. [Ts] M. Tsuji, Potential Theory in Modern Function Theory, Maruzen, Tokyo, 1959. Zbl0087.28401MR114894
  19. [W] J. Wermer, Potential Theory, Springer Lecture Notes in Mathematics, No. 408, Springer Verlag, 1974. Zbl0297.31001MR454033

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.