Percolation on nonamenable products at the uniqueness threshold
Annales de l'I.H.P. Probabilités et statistiques, Volume 36 (2000) no. 3, pp. 395-406.
@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},
     publisher = {Gauthier-Villars},
     volume = {36},
     number = {3},
     year = {2000},
     mrnumber = {1770624},
     zbl = {0965.60094},
     language = {en},
     url = {http://archive.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  - http://archive.numdam.org/item/AIHPB_2000__36_3_395_0/
LA  - en
ID  - AIHPB_2000__36_3_395_0
ER  - 
%0 Journal Article
%A Peres, Yuval
%T Percolation on nonamenable products at the uniqueness threshold
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2000
%P 395-406
%V 36
%N 3
%I Gauthier-Villars
%U http://archive.numdam.org/item/AIHPB_2000__36_3_395_0/
%G en
%F AIHPB_2000__36_3_395_0
Peres, Yuval. Percolation on nonamenable products at the uniqueness threshold. Annales de l'I.H.P. Probabilités et statistiques, Volume 36 (2000) no. 3, pp. 395-406. http://archive.numdam.org/item/AIHPB_2000__36_3_395_0/

[1] Adams S., Lyons R., Amenability, Kazhdan's property and percolation for trees, groups and equivalence relations, Israel J. Math. 75 (1991) 341-370. | MR | Zbl

[2] Benjamini I., Lyons R., Peres Y., Schramm O., Group-invariant percolation on graphs, Geom. Funct. Anal. 9 (1999) 29-66. | MR | Zbl

[3] Benjamini I., Lyons R., Peres Y., Schramm O., Critical percolation on any nonamenable group has no infinite clusters, Ann. Probab. (1999), to appear. | MR | Zbl

[4] Benjamini I., Schramm O., Percolation beyond Zd, many questions and a few answers, Electronic Commun. Probab. 1 (8) (1996) 71-82. | MR | Zbl

[5] Burton R.M., Keane M., Density and uniqueness in percolation, Comm. Math. Phys. 121 (1989) 501-505. | MR | Zbl

[6] Gandolfi A., Keane M.S., Newman C.M., Uniqueness of the infinite component in a random graph with applications to percolation and spin glasses, Probab. Theory Related Fields 92 (1992) 511-527. | MR | Zbl

[7] Grimmett G.R., Newman C.M., 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. | MR | Zbl

[8] Häggström O., Infinite clusters in dependent automorphism invariant percolation on trees, Ann. Probab. 25 (1997) 1423-1436. | MR | Zbl

[9] Häggström O., Peres Y., Monotonicity of uniqueness for percolation on Cayley graphs: all infinite clusters are born simultaneously, Probab. Theory Related Fields 113 (1999) 273-285. | MR | Zbl

[10] Häggström O., Peres Y., Schonmann R.H., 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. | MR | Zbl

[11] Lalley S.P., Percolation on Fuchsian groups, Ann. Inst. H. Poincaré Probab. Statist. 34 (1998) 151-177. | Numdam | MR | Zbl

[12] Liggett T.M., Multiple transition points for the contact process on the binary tree, Ann. Probab. 24 (1996) 1675-1710. | MR | Zbl

[13] Lyons R., Schramm O., Indistinguishability of percolation clusters, Ann. Probab. (1999), to appear. | MR | Zbl

[14] Paterson A.L.T., Amenability, American Mathematical Soc., Providence, 1988. | MR | Zbl

[15] Pemantle R., The contact process on trees, Ann. Probab. 20 (1992) 2089-2116. | MR | Zbl

[16] Pemantle R., Peres Y., Nonamenable products are not treeable, Preprint, 1999, Israel J. Math., to appear. | MR | Zbl

[17] Salvatori M., On the norms of group-invariant transition operators on graphs, J. Theor. Probab. 5 (1992) 563-576. | MR | Zbl

[18] Salzano M., Schonmann R.H., A new proof that for the contact process on homogeneous trees local survival implies complete convergence, Ann. Probab. 26 (1998) 1251-1258. | MR | Zbl

[19] Schonmann R.H., Stability of infinite clusters in supercritical percolation, Probab. Theory Related Fields 113 (1999) 287-300. | MR | Zbl

[20] Schonmann R.H., 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. | MR | Zbl

[21] Zhang Y., The complete convergence theorem of the contact process on trees, Ann. Probab. 24 (1996) 1408-1443. | MR | Zbl