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Volumn 32, Issue 4, 2008, Pages 463-472

Percolation on dual lattices with k-fold symmetry

Author keywords

Critical probability; Percolation; Plane

Indexed keywords


EID: 52349105185     PISSN: 10429832     EISSN: 10982418     Source Type: Journal    
DOI: 10.1002/rsa.20205     Document Type: Article
Times cited : (15)

References (18)
  • 1
    • 0000136970 scopus 로고
    • Sharpness of the phase transition in percolation models
    • M. Aizenman and D. J. Barsky, Sharpness of the phase transition in percolation models, Comm Math Phys 108 (1987), 489-526.
    • (1987) Comm Math Phys , vol.108 , pp. 489-526
    • Aizenman, M.1    Barsky, D.J.2
  • 3
    • 33744934258 scopus 로고    scopus 로고
    • A short proof of the Harris-Kesten Theorem
    • B. Bollobás and O. M. Riordan, A short proof of the Harris-Kesten Theorem, Bull London Math Soc 38 (2006), 470-484.
    • (2006) Bull London Math Soc , vol.38 , pp. 470-484
    • Bollobás, B.1    Riordan, O.M.2
  • 4
    • 34547197519 scopus 로고    scopus 로고
    • Cambridge University Press, Cambridge, x, 323 pp
    • B. Bollobás and O. Riordan, Percolation, Cambridge University Press, Cambridge, 2006, x + 323 pp.
    • (2006) Percolation
    • Bollobás, B.1    Riordan, O.2
  • 5
    • 0000393829 scopus 로고
    • Density and uniqueness in percolation
    • R. M. Burton and M. Keane, Density and uniqueness in percolation, Comm Math Phys 121 (1989), 501-505.
    • (1989) Comm Math Phys , vol.121 , pp. 501-505
    • Burton, R.M.1    Keane, M.2
  • 6
    • 0041855748 scopus 로고
    • On the random-cluster model. I. Introduction and relation to other models
    • C. M. Fortuin and P. W. Kasteleyn, On the random-cluster model. I. Introduction and relation to other models, Physica 57 (1972), 536-564.
    • (1972) Physica , vol.57 , pp. 536-564
    • Fortuin, C.M.1    Kasteleyn, P.W.2
  • 7
    • 0004246476 scopus 로고    scopus 로고
    • 1st edition, Springer, New York, xii, 296 pp
    • G. Grimmett, Percolation, 1st edition, Springer, New York, 1989, xii + 296 pp.
    • (1989) Percolation
    • Grimmett, G.1
  • 8
    • 21344436631 scopus 로고
    • The stochastic random-cluster process and the uniqueness of random-cluster measures
    • G. Grimmett, The stochastic random-cluster process and the uniqueness of random-cluster measures, Ann Probab 23 (1995), 1461-1510.
    • (1995) Ann Probab , vol.23 , pp. 1461-1510
    • Grimmett, G.1
  • 9
    • 0004246476 scopus 로고    scopus 로고
    • 2nd edition, Springer, New York, xiv, 444 pp
    • G. Grimmett, Percolation, 2nd edition, Springer, New York, 1999, xiv + 444 pp.
    • (1999) Percolation
    • Grimmett, G.1
  • 11
    • 0002446794 scopus 로고
    • A lower bound for the critical probability in a certain percolation process
    • T. E. Harris, A lower bound for the critical probability in a certain percolation process, Proc Cambridge Philos Soc 56 (1960), 13-20.
    • (1960) Proc Cambridge Philos Soc , vol.56 , pp. 13-20
    • Harris, T.E.1
  • 12
    • 0002697969 scopus 로고
    • The critical probability of bond percolation on the square lattice equals 1/2
    • H. Kesten, The critical probability of bond percolation on the square lattice equals 1/2, Comm Math Phys 74 (1980), 41-59.
    • (1980) Comm Math Phys , vol.74 , pp. 41-59
    • Kesten, H.1
  • 14
    • 0000819241 scopus 로고
    • Coincidence of critical points in percolation problems
    • M. V. Menshikov, Coincidence of critical points in percolation problems, Soviet Math Dokl 33 (1986), 856-859.
    • (1986) Soviet Math Dokl , vol.33 , pp. 856-859
    • Menshikov, M.V.1
  • 15
    • 34250275869 scopus 로고
    • A note on percolation
    • L. Russo, A note on percolation, Z Wahrsch Verw Gebiete 43 (1978), 39-48.
    • (1978) Z Wahrsch Verw Gebiete , vol.43 , pp. 39-48
    • Russo, L.1
  • 16
    • 34250717783 scopus 로고    scopus 로고
    • Random surfaces
    • vi, 175 pp
    • S. Sheffield, Random surfaces, Astérisque 304 (2005), vi + 175 pp.
    • (2005) Astérisque , vol.304
    • Sheffield, S.1
  • 17
    • 77957093986 scopus 로고    scopus 로고
    • P. D. Seymour and D. J. A. Welsh, Percolation probabilities on the square lattice, in Advances in Graph Theory (Cambridge Combinatorial Conf., Trinity College, Cambridge, 1977, ed. B. Bollobás). Ann Discrete Math 3 (1978), 227-245.
    • P. D. Seymour and D. J. A. Welsh, Percolation probabilities on the square lattice, in Advances in Graph Theory (Cambridge Combinatorial Conf., Trinity College, Cambridge, 1977, ed. B. Bollobás). Ann Discrete Math 3 (1978), 227-245.
  • 18
    • 21144461581 scopus 로고
    • Percolation in the random cluster process and Q-state Potts model
    • D. J. A. Welsh, Percolation in the random cluster process and Q-state Potts model, J Phys A 26(1993), 2471-2483.
    • (1993) J Phys A , vol.26 , pp. 2471-2483
    • Welsh, D.J.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.