@article{AIHPB_1997__33_4_497_0, author = {H\"aggstr\"om, Olle and Peres, Yuval and Steif, Jeffrey E.}, title = {Dynamical {Percolation}}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, pages = {497--528}, publisher = {Gauthier-Villars}, volume = {33}, number = {4}, year = {1997}, mrnumber = {1465800}, zbl = {0894.60098}, language = {en}, url = {http://archive.numdam.org/item/AIHPB_1997__33_4_497_0/} }
TY - JOUR AU - Häggström, Olle AU - Peres, Yuval AU - Steif, Jeffrey E. TI - Dynamical Percolation JO - Annales de l'I.H.P. Probabilités et statistiques PY - 1997 SP - 497 EP - 528 VL - 33 IS - 4 PB - Gauthier-Villars UR - http://archive.numdam.org/item/AIHPB_1997__33_4_497_0/ LA - en ID - AIHPB_1997__33_4_497_0 ER -
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://archive.numdam.org/item/AIHPB_1997__33_4_497_0/
[1] Simultaneous uniqueness of infinite clusters in stationary random labeled graphs, Commun. Math. Phys., Vol. 168, 1995, pp. 39-55. | MR | Zbl
,[2] Branching Processes, Springer-Verlag, New York, 1972. | MR | Zbl
and ,[3] Mathematical Theory of Reliability, Wiley, New York, 1965. | MR | Zbl
and ,[4] Martin capacity for Markov chains, Ann. Probab., Vol. 23, 1995, pp. 1332-1346. | MR | Zbl
, and ,[5] Random Walks and Electric Networks, Mathematical Assoc. of America, Washington, D. C., 1984. | MR | Zbl
and ,[6] Markov Processes-Characterization and Convergence, John Wiley & Sons, New York., 1986. | Zbl
and ,[7] An Introduction to Probability Theory and its Applications, Volume 2. John Wiley and Sons: New York, 1966. | MR | Zbl
,[8] Potential d'équilibre et capacité des ensembles, Thesis, Lund, 1935.
,[9] 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] Percolation, Springer-Verlag, New York, 1989. | MR | Zbl
,[11] 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
and ,[12] A correlation inequality for Markov processes in partially ordered spaces, Ann. Probab., Vol. 5, 1977, pp. 451-454. | MR | Zbl
,[13] Some random series of functions, Second edition, Cambridge University Press: Cambridge, 1985. | MR | Zbl
,[14] 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] Scaling relations for 2D-percolation, Commun. Math. Phys., Vol. 109, 1987, pp. 109-156. | MR | Zbl
,[16] Strict inequalites for some critical exponents in 2D-percolation, J. Statist. Phys., Vol. 46, 1987, pp. 1031-1055. | MR | Zbl
and ,[17] 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] Interacting Particle Systems, Springer, New York, 1985. | MR | Zbl
,[19] Random walks and percolation on trees, Ann. Probab., Vol. 18, 1990, pp. 931-958. | MR | Zbl
,[20] Random walks, capacity, and percolation on trees, Ann. Probab., Vol. 20, 1992, pp. 2043-2088. | MR | Zbl
,[21] Critical random walk in random environment on trees, Ann. Probab., Vol. 23, 1995a, pp. 105-140. | MR | Zbl
and ,[22] Galton-Watson trees with the same mean have the same polar sets, Ann. Probab., Vol. 23, 1995b, pp. 1102-1124. | MR | Zbl
and ,[23] On the existence of self-intersections for quasi-every Brownian path in space, Ann. Probab., Vol. 17, 1989, pp. 482-502. | MR | Zbl
,[24] Intersection-equivalence of Brownian paths and certain branching processes, Commun. Math. Phys., Vol. 177, 1996, pp. 417-434. | MR | Zbl
,[25] Markov Processes. Structure and Asymptotic Behavior, Springer, New York, 1971. | MR | Zbl
,[26] Covering the circle with random arcs, Israel J. Math., Vol. 11, 1972, pp. 328-345. | MR | Zbl
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