A new lower bound for the critical probability of site percolation on the square lattice

Random Structures and Algorithms

Volumn 8, Issue 3, 1996, Pages 199-212

  Van Den Berg, J ^a   Ermakov, A ^a  

^a CWI   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030303839     PISSN: 10429832     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1098-2418(199605)8:3<199::AID-RSA4>3.0.CO;2-T     Document Type: Article

References (16)

1. P. Balister, B. Bollobás, and A. Stacey, Improved upper bounds for the critical probability of oriented percolation in two dimensions, Random Struct. Alg., 5, 573-589 (1994).
2. M. E. Fisher, Critical probabilities for cluster size and percolation problems, J. Math. Phys., 2, 620-627 (1961).
3. G. Grimmett, Percolation, Springer-Verlag, New York, 1989.
4. J. M. Hammersley, Percolation processes. Lower bounds for the critical probability, Ann. Math. Stat., 28, 790-795 (1957).
5. J. M. Hammersley, Comparison of atom and bond percolation, J. Math. Phys., 2, 728-733 (1961).
6. T. E. Harris, A lower bound for the critical probability in a certain percolation process, Proc. Camb. Phil. Soc., 56, 13-20 (1960).
7. Y. Higuchi, Coexistence of the infinite (*) clusters: a remark on the square lattice site percolation, Z.W., 61, 75-81 (1982).
8. H. Kesten, The critical probability of bond percolation on the square lattice equals 1/2, Commun. Math. Phys., 74, 41-59 (1980).
9. H. Kesten, Percolation theory and first-passage percolation, Ann. Probab., 15, 1231-1271 (1987).
10. T. M. Liggett, Interacting Particle Systems, Springer-Verlag, New York, 1985.
11. T. Łuczak and J. C. Wierman, Critical probability bounds for two-dimensional site percolation models, J. Phys. A, 21, 3131-3138 (1988).
12. M. V. Menshikov and K. D. Pelikh, Mat. Zametki, 46, 38-47 [Engl. Transl.: Percolation with several defect types. An estimate of critical probability for a square lattice, Math. Notes Acad. Sci. USSR, 46(4), 778-785 (1990)].
13. M. V. Menshikov and K. D. Pelikh, Mat. Zametki, 46, 38-47 [Engl. Transl.: Percolation with several defect types. An estimate of critical probability for a square lattice, Math. Notes Acad. Sci. USSR, 46(4), 778-785 (1990)].
14. B. Tóth, A lower bound for the critical probability of the square lattice site percolation, Z.W., 69, 19-22 (1985).
15. J. van den Berg and C. Maes, Disagreement percolation in the study of Markov fields, Ann. Probab., 22, 749-763 (1994).
16. S. A. Zuev, A lower bound for the percolation threshold for the square lattice, Moscow Univ. Math. Bull., 43(5), 59-61 (66-69 in translation) (1988).