Dynamical Percolation
Annales de l'I.H.P. Probabilités et statistiques, Tome 33 (1997) no. 4, pp. 497-528.
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     title = {Dynamical {Percolation}},
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     language = {en},
     url = {http://www.numdam.org/item/AIHPB_1997__33_4_497_0/}
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Häggström, Olle; Peres, Yuval; Steif, Jeffrey E. Dynamical Percolation. Annales de l'I.H.P. Probabilités et statistiques, Tome 33 (1997) no. 4, pp. 497-528. http://www.numdam.org/item/AIHPB_1997__33_4_497_0/

[1] K. Alexander, Simultaneous uniqueness of infinite clusters in stationary random labeled graphs, Commun. Math. Phys., Vol. 168, 1995, pp. 39-55. | MR | Zbl

[2] K. Athreya and P. Ney, Branching Processes, Springer-Verlag, New York, 1972. | MR | Zbl

[3] R.E. Barlow and F. Proschan, Mathematical Theory of Reliability, Wiley, New York, 1965. | MR | Zbl

[4] I. Benjamini, R. Pemantle and Y. Peres, Martin capacity for Markov chains, Ann. Probab., Vol. 23, 1995, pp. 1332-1346. | MR | Zbl

[5] P. Doyle and J.L. Snell, Random Walks and Electric Networks, Mathematical Assoc. of America, Washington, D. C., 1984. | MR | Zbl

[6] S.N. Ethier and T.G. Kurtz, Markov Processes-Characterization and Convergence, John Wiley & Sons, New York., 1986. | Zbl

[7] W. Feller, An Introduction to Probability Theory and its Applications, Volume 2. John Wiley and Sons: New York, 1966. | MR | Zbl

[8] O. Frostman, Potential d'équilibre et capacité des ensembles, Thesis, Lund, 1935.

[9] M. Fukushima, Basic properties of Brownian motion and a capacity on the Wiener space, J. Math. Soc. Japan, Vol. 36, 1984, pp. 161-175. | MR | Zbl

[10] G. Grimmett, Percolation, Springer-Verlag, New York, 1989. | MR | Zbl

[11] T. Hara and G. Slade, Mean field behavior and the lace expansion, in Probability Theory and Phase Transitions, (ed. G. Grimmett), Proceedings of the NATO ASI meeting in Cambridge 1993, Kluwer, 1994. | MR | Zbl

[12] T.E. Harris, A correlation inequality for Markov processes in partially ordered spaces, Ann. Probab., Vol. 5, 1977, pp. 451-454. | MR | Zbl

[13] J.P. Kahane, Some random series of functions, Second edition, Cambridge University Press: Cambridge, 1985. | MR | Zbl

[14] H. Kesten, The critical probability of bond percolation on the square lattice equals 1/2, Commun. Math. Phys., Vol. 74, 1980, pp. 41-59. | MR | Zbl

[15] H. Kesten, Scaling relations for 2D-percolation, Commun. Math. Phys., Vol. 109, 1987, pp. 109-156. | MR | Zbl

[16] H. Kesten and Y. Zhang, Strict inequalites for some critical exponents in 2D-percolation, J. Statist. Phys., Vol. 46, 1987, pp. 1031-1055. | MR | Zbl

[17] J.-F. Le Gall, Some properties of planar Brownian motion, École d'été de probabilités de Saint-Flour XX, Lecture Notes in Math., Vol. 1527, 1992, pp. 111-235. Springer, New York. | MR | Zbl

[18] T.M. Liggett, Interacting Particle Systems, Springer, New York, 1985. | MR | Zbl

[19] R. Lyons, Random walks and percolation on trees, Ann. Probab., Vol. 18, 1990, pp. 931-958. | MR | Zbl

[20] R. Lyons, Random walks, capacity, and percolation on trees, Ann. Probab., Vol. 20, 1992, pp. 2043-2088. | MR | Zbl

[21] R. Pemantle and Y. Peres, Critical random walk in random environment on trees, Ann. Probab., Vol. 23, 1995a, pp. 105-140. | MR | Zbl

[22] R. Pemantle and Y. Peres, Galton-Watson trees with the same mean have the same polar sets, Ann. Probab., Vol. 23, 1995b, pp. 1102-1124. | MR | Zbl

[23] M.D. Penrose, On the existence of self-intersections for quasi-every Brownian path in space, Ann. Probab., Vol. 17, 1989, pp. 482-502. | MR | Zbl

[24] Y. Peres, Intersection-equivalence of Brownian paths and certain branching processes, Commun. Math. Phys., Vol. 177, 1996, pp. 417-434. | MR | Zbl

[25] M. Rosenblatt, Markov Processes. Structure and Asymptotic Behavior, Springer, New York, 1971. | MR | Zbl

[26] L.A. Shepp, Covering the circle with random arcs, Israel J. Math., Vol. 11, 1972, pp. 328-345. | MR | Zbl