@article{AIHPB_2007__43_5_509_0, author = {Van der Hofstad, Remco and den Hollander, Frank and Slade, Gordon}, title = {The survival probability for critical spread-out oriented percolation above $4+1$ dimensions. II. Expansion}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, volume = {43}, year = {2007}, pages = {509-570}, doi = {10.1016/j.anihpb.2006.09.002}, mrnumber = {2347096}, zbl = {1134.60063}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPB_2007__43_5_509_0} }
Van der Hofstad, Remco; den Hollander, Frank; Slade, Gordon. The survival probability for critical spread-out oriented percolation above $4+1$ dimensions. II. Expansion. Annales de l'I.H.P. Probabilités et statistiques, Tome 43 (2007) pp. 509-570. doi : 10.1016/j.anihpb.2006.09.002. http://gdmltest.u-ga.fr/item/AIHPB_2007__43_5_509_0/
[1] Percolation critical exponents under the triangle condition, Ann. Probab. 19 (1991) 1520-1536. | MR 1127713 | Zbl 0747.60093
, ,[2] The critical contact process dies out, Ann. Probab. 18 (1990) 1462-1482. | MR 1071804 | Zbl 0718.60109
, ,[3] Percolation, second ed., Springer, Berlin, 1999. | MR 1707339 | Zbl 0926.60004
,[4] Directed percolation and random walk, in: (Ed.), In and Out of Equilibrium, Birkhäuser, Boston, 2002, pp. 273-297. | MR 1901958 | Zbl 1010.60087
, ,[5] Mean-field critical behaviour for percolation in high dimensions, Comm. Math. Phys. 128 (1990) 333-391. | MR 1043524 | Zbl 0698.60100
, ,[6] The scaling limit of the incipient infinite cluster in high-dimensional percolation. I. Critical exponents, J. Stat. Phys. 99 (2000) 1075-1168. | MR 1773141 | Zbl 0968.82016
, ,[7] R. van der Hofstad, F. den Hollander, G. Slade, The survival probability for critical spread-out oriented percolation above dimensions. I. Induction. Preprint, 2005. Probab. Theory Related Fields, in press. | MR 2299712 | Zbl 1130.60094
[8] Construction of the incipient infinite cluster for spread-out oriented percolation above dimensions, Comm. Math. Phys. 231 (2002) 435-461. | MR 1946445 | Zbl 1013.82017
, , ,[9] Gaussian scaling for the critical spread-out contact process above the upper critical dimension, Electron. J. Probab. 9 (2004) 710-769. | MR 2110017 | Zbl 1077.60076
, ,[10] Critical points for spread-out self-avoiding walk, percolation and the contact process, Probab. Theory Related Fields 132 (2005) 438-470. | MR 2197108 | Zbl 1083.60080
, ,[11] R. van der Hofstad, A. Sakai, Convergence of the critical finite-range contact process to super-Brownian motion above the upper critical dimension. I. The higher-point functions, in preparation. | Zbl 1226.60139
[12] R. van der Hofstad, A. Sakai, Convergence of the critical finite-range contact process to super-Brownian motion above the upper critical dimension. II. The survival probability, in preparation.
[13] A generalised inductive approach to the lace expansion, Probab. Theory Related Fields 122 (2002) 389-430. | MR 1892852 | Zbl 1002.60095
, ,[14] Convergence of critical oriented percolation to super-Brownian motion above dimensions, Ann. Inst. H. Poincaré Probab. Statist. 39 (2003) 415-485. | Numdam | MR 1978987 | Zbl 1020.60099
, ,[15] The Self-Avoiding Walk, Birkhäuser, Boston, 1993. | MR 1197356 | Zbl 0780.60103
, ,[16] Triangle condition for oriented percolation in high dimensions, Ann. Probab. 21 (1993) 1809-1844. | MR 1245291 | Zbl 0806.60097
, ,[17] Mean-field critical behavior for the contact process, J. Stat. Phys. 104 (2001) 111-143. | MR 1851386 | Zbl 1019.82012
,[18] The Lace Expansion and its Applications, Lecture Notes in Mathematics, vol. 1879, Springer, 2006, Ecole d'Eté Probabilit. Saint-Flour. | MR 2239599 | Zbl 1113.60005
,