Stochastic domination : the contact process, Ising models and FKG measures
Annales de l'I.H.P. Probabilités et statistiques, Tome 42 (2006) no. 2, pp. 223-243.
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     title = {Stochastic domination : the contact process, {Ising} models and {FKG} measures},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {223--243},
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}
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Liggett, Thomas M.; Steif, Jeffrey E. Stochastic domination : the contact process, Ising models and FKG measures. Annales de l'I.H.P. Probabilités et statistiques, Tome 42 (2006) no. 2, pp. 223-243. doi : 10.1016/j.anihpb.2005.04.002. http://www.numdam.org/articles/10.1016/j.anihpb.2005.04.002/

[1] V. Belitsky, P. Ferrari, N. Konno, T.M. Liggett, A strong correlation inequality for contact processes and oriented percolation, Stochastic Process Appl. 67 (1997) 213-225. | MR | Zbl

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

[3] J. van den Berg, O. Häggström, J. Kahn, Some conditional correlation inequalities for percolation and related processes, Rand. Structures Algorithms, in press. | MR | Zbl

[4] J. Bricmont, J.L. Lebowitz, C. Maes, Percolation in strongly correlated systems: the massless Gaussian free field, J. Statist. Phys. 48 (1987) 1249-1268. | MR | Zbl

[5] E.I. Broman, J.E. Steif, Dynamical stability of percolation for some interacting particle systems and ϵ-stability, Ann. Probab., in press. | Zbl

[6] H.O. Georgii, Gibbs Measures and Phase Transitions, de Gruyter, 1988. | MR | Zbl

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

[8] R.A. Holley, T.M. Liggett, The survival of contact processes, Ann. Probab. 6 (1978) 198-206. | MR | Zbl

[9] T.M. Liggett, Interacting Particle Systems, Springer, 1985. | MR | Zbl

[10] T.M. Liggett, Survival and coexistence in interacting particle systems, in: Probability and Phase Transition, Kluwer Academic, 1994, pp. 209-226. | MR | Zbl

[11] T.M. Liggett, Survival of discrete time growth models, with applications to oriented percolation, Ann. Appl. Probab. 5 (1995) 613-636. | MR | Zbl

[12] T.M. Liggett, Stochastic Interacting Systems: Contact, Voter and Exclusion Processes, Springer, 1999. | MR | Zbl

[13] T.M. Liggett, R.H. Schonmann, A.M. Stacey, Domination by product measures, Ann. Probab. 25 (1997) 71-95. | MR | Zbl

[14] R. Lyons, J.E. Steif, Stationary determinantal processes: phase multiplicity, Bernoullicity, entropy, and domination, Duke Math. J. 120 (2003) 515-575. | MR | Zbl

[15] C. Maes, F. Redig, S. Shlosman, A. Van Moffaert, Percolation, path large deviations and weak Gibbsianity, Comm. Math. Phys. 209 (2000) 517-545. | MR | Zbl

[16] R.H. Schonmann, Second order large deviation estimates for ferromagnetic systems in the phase coexistence region, Comm. Math. Phys. 112 (1987) 409-422. | MR

[17] C.J. Thompson, Mathematical Statistical Mechanics, Princeton University Press, 1972. | MR | Zbl

[18] J.C. Wierman, Substitution method critical probability bounds for the square lattice site percolation model, Combin. Probab. Comput. 4 (1995) 181-188. | MR | Zbl

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