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Volumn 11, Issue 6, 2002, Pages 629-643

An improved upper bound for the hexagonal lattice site percolation critical probability

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL MODELS; POLYNOMIALS; PROBABILITY; PROBABILITY DENSITY FUNCTION; THEOREM PROVING;

EID: 0036026965     PISSN: 09635483     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0963548302005345     Document Type: Article
Times cited : (16)

References (17)
  • 5
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    • Percolation processes: Lower bounds for the critical probability
    • Hammersley, J. M. 1957 Percolation processes: Lower bounds for the critical probability. Ann. Math. Statist. 28 790-795.
    • (1957) Ann. Math. Statist. , vol.28 , pp. 790-795
    • Hammersley, J.M.1
  • 6
    • 0000574028 scopus 로고
    • Comparison of atom and bond percolation
    • Hammersley, J. M. (1961) Comparison of atom and bond percolation. J. Math. Phys. 2 728-733.
    • (1961) J. Math. Phys. , vol.2 , pp. 728-733
    • Hammersley, J.M.1
  • 8
    • 0000706435 scopus 로고
    • Critical probability bounds for two-dimensional site percolation models
    • Luczak, T. and Wierman, J. C. (1988) Critical probability bounds for two-dimensional site percolation models. J. Phys. A: Math. Gen. 21, 3131-3138.
    • (1988) J. Phys. A: Math. Gen. , vol.21 , pp. 3131-3138
    • Luczak, T.1    Wierman, J.C.2
  • 9
    • 34250413470 scopus 로고
    • A generalization of the FKG inequalities
    • Preston, C. J. (1974) A generalization of the FKG inequalities. Comm. Math. Phys. 36 233-241.
    • (1974) Comm. Math. Phys. , vol.36 , pp. 233-241
    • Preston, C.J.1
  • 11
    • 0012833024 scopus 로고
    • Relations between site percolation thresholds
    • Shalitin, D. (1982) Relations between site percolation thresholds. J. Statist. Phys. 28 99-110.
    • (1982) J. Statist. Phys. , vol.28 , pp. 99-110
    • Shalitin, D.1
  • 13
    • 29544441737 scopus 로고
    • Exact critical percolation probabilities for site and bond problems in two dimensions
    • Sykes, M. F. and Essam, J. W. (1964) Exact critical percolation probabilities for site and bond problems in two dimensions. J. Math. Phys. 5 1117-1127.
    • (1964) J. Math. Phys. , vol.5 , pp. 1117-1127
    • Sykes, M.F.1    Essam, J.W.2
  • 14
    • 0000095499 scopus 로고
    • Bond percolation on the honeycomb and triangular lattices
    • Wierman, J. C. (1981) Bond percolation on the honeycomb and triangular lattices. Adv. Appl. Probab. 13 298-313.
    • (1981) Adv. Appl. Probab. , vol.13 , pp. 298-313
    • Wierman, J.C.1
  • 15
    • 0000901150 scopus 로고
    • Bond percolation critical probability bounds for the Kagomé lattice by a substitution method
    • (G. Grimmett and D. J. A. Welsh, eds), Oxford University Press
    • Wierman, J. C. (1990) Bond percolation critical probability bounds for the Kagomé lattice by a substitution method. In Disorder in Physical Systems (G. Grimmett and D. J. A. Welsh, eds), Oxford University Press, pp. 349-360.
    • (1990) Disorder in Physical Systems , pp. 349-360
    • Wierman, J.C.1
  • 16
    • 84971722474 scopus 로고
    • Equality of the bond percolation critical exponents for two pairs of dual lattices
    • Wierman, J. C. (1992) Equality of the bond percolation critical exponents for two pairs of dual lattices. Combin. Probab. Comput. 1 95-105.
    • (1992) Combin. Probab. Comput. , vol.1 , pp. 95-105
    • Wierman, J.C.1
  • 17
    • 84974277206 scopus 로고
    • Substitution method critical probability bounds for the square lattice site perlocation model
    • Wierman, J. C. (1995) Substitution method critical probability bounds for the square lattice site percolation model. Combin. Probab. Comput. 4 181-188.
    • (1995) Combin. Probab. Comput. , vol.4 , pp. 181-188
    • Wierman, J.C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.