A large deviation result for the subcritical Bernoulli percolation
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 14 (2005) no. 2, p. 201-214
@article{AFST_2005_6_14_2_201_0,
     author = {Couronn\'e, Olivier},
     title = {A large deviation result for the subcritical Bernoulli percolation},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
     address = {Toulouse},
     volume = {Ser. 6, 14},
     number = {2},
     year = {2005},
     pages = {201-214},
     zbl = {1086.60530},
     mrnumber = {2141181},
     language = {en},
     url = {http://www.numdam.org/item/AFST_2005_6_14_2_201_0}
}
Couronné, Olivier. A large deviation result for the subcritical Bernoulli percolation. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 14 (2005) no. 2, pp. 201-214. http://www.numdam.org/item/AFST_2005_6_14_2_201_0/

[1] Van Den Berg (J.), Kesten (H.) . - Inequalities with applications to percolation and reliability theory, J. Appl. Prob. 22, p. 556-569 (1985). | MR 799280 | Zbl 0571.60019

[2] Castaing ( C. ) , Valadier ( M.). - Convex analysis and measurable multifunctions , Lectures Notes in Math 580, Springer (1977). | MR 467310 | Zbl 0346.46038

[3] Cerf (R.) . - Large Deviations of the Finite Cluster Shape for Two-Dimensional Percolation in the Hausdorff and L1 Metric, J. Theor. Prob. 13 (2000). | MR 1777542 | Zbl 0974.60089

[4] Cerf (R.) . - Large deviation for three-dimensional supercritical percolation, Astérisque 267 (2000). | MR 1774341 | Zbl 0962.60002

[5] Dembo (A.) , Zeitouni ( O.). - Large deviations techniques and applications , 2nd edition, Springer, New York (1998). | MR 1619036 | Zbl 0896.60013

[6] Falconer ( K.J. ). - The Geometry of Fractals Sets , Cambridge (1986). | MR 867284 | Zbl 0587.28004

[7] Fortuin (C. ), Kasteleyn (P.), Ginibre (J.). - Correlation inequalities on some partially ordered sets, Commun. Math. Phys. 22, 89-103 (1971). | MR 309498 | Zbl 0346.06011

[8] Freidlin ( M.I. ), Wentzell (A.D.). - Random perturbations of dynamical systems, Springer-Verlag, New York (1984). | MR 722136 | Zbl 0522.60055

[9] Grimmett ( G. ). - Percolation, Second Edition, Springer 321 (1999). | MR 1707339 | Zbl 0926.60004

[10] Harris (T.E. ) . - A lower bound for the critical probability in a certain percolation process, Proc. Camb. Phil. Soc. 56, 13-20 (1960). | MR 115221 | Zbl 0122.36403

[11] Kovchegov ( Y. ), Sheffield (S.). - Linear speed large deviations for percolation clusters, Preprint (2003). | MR 2042757 | Zbl 1060.60097