no. 5
Markov chain intersections and the loop-erased walk
Annales de l'I.H.P. Probabilités et statistiques, Tome 39 (2003) no. 5, pp. 779-791. 
@article{AIHPB_2003__39_5_779_0,
     author = {Lyons, Russell and Peres, Yuval and Schramm, Oded},
     title = {Markov chain intersections and the loop-erased walk},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {779--791},
     publisher = {Elsevier},
     volume = {39},
     number = {5},
     year = {2003},
     doi = {10.1016/S0246-0203(03)00033-5},
     mrnumber = {1997212},
     zbl = {1030.60035},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/S0246-0203(03)00033-5/}
}
TY  - JOUR
AU  - Lyons, Russell
AU  - Peres, Yuval
AU  - Schramm, Oded
TI  - Markov chain intersections and the loop-erased walk
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 2003
SP  - 779
EP  - 791
VL  - 39
IS  - 5
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/S0246-0203(03)00033-5/
DO  - 10.1016/S0246-0203(03)00033-5
LA  - en
ID  - AIHPB_2003__39_5_779_0
ER  - 
%0 Journal Article
%A Lyons, Russell
%A Peres, Yuval
%A Schramm, Oded
%T Markov chain intersections and the loop-erased walk
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2003
%P 779-791
%V 39
%N 5
%I Elsevier
%U http://www.numdam.org/articles/10.1016/S0246-0203(03)00033-5/
%R 10.1016/S0246-0203(03)00033-5
%G en
%F AIHPB_2003__39_5_779_0
Lyons, Russell; Peres, Yuval; Schramm, Oded. Markov chain intersections and the loop-erased walk. Annales de l'I.H.P. Probabilités et statistiques, Tome 39 (2003) no. 5, pp. 779-791. doi : 10.1016/S0246-0203(03)00033-5. http://www.numdam.org/articles/10.1016/S0246-0203(03)00033-5/

[1] I. Benjamini, R. Lyons, Y. Peres, O. Schramm, Uniform spanning forests, Ann. Probab. 29 (2001) 1-65. | MR | Zbl

[2] D.L. Burkholder, B.J. Davis, R.F. Gundy, Integral inequalities for convex functions of operators on martingales, in: Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley 1970/1971), Vol. II: Probability Theory, University California Press, Berkeley, 1972, pp. 223-240. | MR | Zbl

[3] P. Erdo&Amp;#X030B;S, S.J. Taylor, Some intersection properties of random walk paths, Acta Math. Acad. Sci. Hungar. 11 (1960) 231-248. | MR | Zbl

[4] P.J. Fitzsimmons, T. Salisbury, Capacity and energy for multiparameter Markov processes, Ann. Inst. H. Poincaré Probab. Statist. 25 (1989) 325-350. | Numdam | MR | Zbl

[5] O. Häggström, Random-cluster measures and uniform spanning trees, Stochastic Process. Appl. 59 (1995) 267-275. | MR | Zbl

[6] N. James, Ph.D. Thesis, University of California, Berkeley, 1996.

[7] N. James, Y. Peres, Cutpoints and exchangeable events for random walks, Teor. Veroyatnost. i Primenen. 41 (1996) 854-868, Reproduced in , Theory Probab. Appl. 41 (1997) 666-677. | MR | Zbl

[8] J.-P. Kahane, Some Random Series of Functions, Cambridge University Press, Cambridge, 1985. | MR | Zbl

[9] G. Lawler, Intersections of Random Walks, Birkhäuser, Boston, 1991. | MR | Zbl

[10] G. Lawler, Loop-erased walks intersect infinitely often in four dimensions, Electron. Comm. Probab. 3 (1998) 35-42. | MR | Zbl

[11] J.-F. Le Gall, J. Rosen, The range of stable random walks, Ann. Probab. 19 (1991) 650-705. | MR | Zbl

[12] R. Pemantle, Choosing a spanning tree for the integer lattice uniformly, Ann. Probab. 19 (1991) 1559-1574. | MR | Zbl

[13] T. Salisbury, Energy, and intersections of Markov chains, in: Aldous D., Pemantle R. (Eds.), Random Discrete Structures, The IMA Volumes in Mathematics and its Applications, 76, Springer-Verlag, New York, 1996, pp. 213-225. | MR | Zbl

[14] D.B. Wilson, Generating random spanning trees more quickly than the cover time, in: Proceedings of the Twenty-eighth Annual ACM Symposium on the Theory of Computing (Philadelphia, PA, 1996), ACM, New York, 1996, pp. 296-303. | MR | Zbl

[15] W. Woess, Random Walks on Infinite Graphs and Groups, Cambridge Tracts in Math., 138, Cambridge University Press, Cambridge, 2000. | MR | Zbl

Cité par Sources :