@article{AIHPB_2000__36_3_395_0,
author = {Peres, Yuval},
title = {Percolation on nonamenable products at the uniqueness threshold},
journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
pages = {395--406},
year = {2000},
publisher = {Gauthier-Villars},
volume = {36},
number = {3},
mrnumber = {1770624},
zbl = {0965.60094},
language = {en},
url = {https://www.numdam.org/item/AIHPB_2000__36_3_395_0/}
}
TY - JOUR AU - Peres, Yuval TI - Percolation on nonamenable products at the uniqueness threshold JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2000 SP - 395 EP - 406 VL - 36 IS - 3 PB - Gauthier-Villars UR - https://www.numdam.org/item/AIHPB_2000__36_3_395_0/ LA - en ID - AIHPB_2000__36_3_395_0 ER -
Peres, Yuval. Percolation on nonamenable products at the uniqueness threshold. Annales de l'I.H.P. Probabilités et statistiques, Tome 36 (2000) no. 3, pp. 395-406. https://www.numdam.org/item/AIHPB_2000__36_3_395_0/
[1] , , Amenability, Kazhdan's property and percolation for trees, groups and equivalence relations, Israel J. Math. 75 (1991) 341-370. | Zbl | MR
[2] , , , , Group-invariant percolation on graphs, Geom. Funct. Anal. 9 (1999) 29-66. | Zbl | MR
[3] Benjamini I., , , , Critical percolation on any nonamenable group has no infinite clusters, Ann. Probab. (1999), to appear. | Zbl | MR
[4] Benjamini I., , Percolation beyond Zd, many questions and a few answers, Electronic Commun. Probab. 1 (8) (1996) 71-82. | Zbl | MR
[5] , , Density and uniqueness in percolation, Comm. Math. Phys. 121 (1989) 501-505. | Zbl | MR
[6] , , , Uniqueness of the infinite component in a random graph with applications to percolation and spin glasses, Probab. Theory Related Fields 92 (1992) 511-527. | Zbl | MR
[7] , , Percolation in oo + 1 dimensions, in: Grimmett G.R., Welsh D.J.A. (Eds.), Disorder in Physical Systems, Clarendon Press, Oxford, 1990, pp. 167-190. | Zbl | MR
[8] , Infinite clusters in dependent automorphism invariant percolation on trees, Ann. Probab. 25 (1997) 1423-1436. | Zbl | MR
[9] , , Monotonicity of uniqueness for percolation on Cayley graphs: all infinite clusters are born simultaneously, Probab. Theory Related Fields 113 (1999) 273-285. | Zbl | MR
[10] , , , Percolation on transitive graphs as a coalescent process: relentless merging followed by simultaneous uniqueness, in: Bramson M., Durrett R. (Eds.), Perplexing Probability Problems: Papers in Honor of Harry Kesten, Birkhäuser, 1999, pp. 69-90. | Zbl | MR
[11] , Percolation on Fuchsian groups, Ann. Inst. H. Poincaré Probab. Statist. 34 (1998) 151-177. | Zbl | MR | Numdam
[12] , Multiple transition points for the contact process on the binary tree, Ann. Probab. 24 (1996) 1675-1710. | Zbl | MR
[13] , , Indistinguishability of percolation clusters, Ann. Probab. (1999), to appear. | Zbl | MR
[14] , Amenability, American Mathematical Soc., Providence, 1988. | Zbl | MR
[15] , The contact process on trees, Ann. Probab. 20 (1992) 2089-2116. | Zbl | MR
[16] , , Nonamenable products are not treeable, Preprint, 1999, Israel J. Math., to appear. | Zbl | MR
[17] , On the norms of group-invariant transition operators on graphs, J. Theor. Probab. 5 (1992) 563-576. | Zbl | MR
[18] , , A new proof that for the contact process on homogeneous trees local survival implies complete convergence, Ann. Probab. 26 (1998) 1251-1258. | Zbl | MR
[19] , Stability of infinite clusters in supercritical percolation, Probab. Theory Related Fields 113 (1999) 287-300. | Zbl | MR
[20] , Percolation in ∞ + 1 dimensions at the uniqueness threshold, in: Bramson M., Durrett R. (Eds.), Perplexing Probability Problems: Papers in Honor of H. Kesten, Birkhäuser, 1999, pp. 53-67. | Zbl | MR
[21] , The complete convergence theorem of the contact process on trees, Ann. Probab. 24 (1996) 1408-1443. | Zbl | MR





