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Volumn 15, Issue 3-4, 1999, Pages 368-413

Uniform boundedness of critical crossing probabilities implies hyperscaling

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EID: 0033459005     PISSN: 10429832     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1098-2418(199910/12)15:3/4<368::AID-RSA9>3.0.CO;2-B     Document Type: Article
Times cited : (37)

References (32)
  • 1
    • 0031561930 scopus 로고    scopus 로고
    • On the number of incipient spanning clusters
    • M. Aizenman, On the number of incipient spanning clusters, Nucl Phys B, 485 (1997), 551-582.
    • (1997) Nucl Phys B , vol.485 , pp. 551-582
    • Aizenman, M.1
  • 2
    • 0040873123 scopus 로고    scopus 로고
    • Private communication
    • K. Alexander, Private communication, 1996.
    • (1996)
    • Alexander, K.1
  • 3
    • 0002190594 scopus 로고
    • On a sharp transition from area law to perimeter law in a system of random surfaces
    • M. Aizenman, J. T. Chayes, L. Chayes, J. Fröhlich, and L. Russo, On a sharp transition from area law to perimeter law in a system of random surfaces, Commun Math Phys, 92 (1983), 19-69.
    • (1983) Commun Math Phys , vol.92 , pp. 19-69
    • Aizenman, M.1    Chayes, J.T.2    Chayes, L.3    Fröhlich, J.4    Russo, L.5
  • 4
    • 0010788259 scopus 로고
    • Multiplicity of the infinite clusters in percolation above six dimensions
    • L. de Arcangelis, Multiplicity of the infinite clusters in percolation above six dimensions, J Phys A: Math Gen, 20 (1987), 3057-3061.
    • (1987) J Phys A: Math Gen , vol.20 , pp. 3057-3061
    • De Arcangelis, L.1
  • 7
    • 0022116584 scopus 로고
    • Inequalities with applications to percolation and reliability
    • J. van den Berg and H. Kesten, Inequalities with applications to percolation and reliability, J Appl Probab 22 (1985), 556-569.
    • (1985) J Appl Probab , vol.22 , pp. 556-569
    • Van Den Berg, J.1    Kesten, H.2
  • 8
    • 0004592957 scopus 로고
    • The probability distribution of the percolation threshold in a large system
    • L. Berlyand and J. Wehr, The probability distribution of the percolation threshold in a large system, J Phys A: Math Gen, 28 (1995), 7127-7133.
    • (1995) J Phys A: Math Gen , vol.28 , pp. 7127-7133
    • Berlyand, L.1    Wehr, J.2
  • 9
    • 0031116539 scopus 로고    scopus 로고
    • Nongaussian limiting behavior of the percolation threshold in a large system
    • L. Berlyand and J. Wehr, Nongaussian limiting behavior of the percolation threshold in a large system, Commun Math Phys, 185 (1997), 73-92.
    • (1997) Commun Math Phys , vol.185 , pp. 73-92
    • Berlyand, L.1    Wehr, J.2
  • 10
    • 0007093634 scopus 로고
    • Percolation and random media
    • Les Houches, Session XLIII, K. Osterwalder and R. Stora (Editors), Elsevier, Amsterdam
    • J. T. Chayes and L. Chayes, Percolation and random media, in Random Systems and Gauge Theories, Les Houches, Session XLIII, K. Osterwalder and R. Stora (Editors), Elsevier, Amsterdam, 1984, pp. 1001-1142.
    • (1984) Random Systems and Gauge Theories , pp. 1001-1142
    • Chayes, J.T.1    Chayes, L.2
  • 11
    • 0001302057 scopus 로고
    • Bulk transport properties and critical exponent inequalities for random resistor and flow networks
    • J. T. Chayes and L. Chayes, Bulk transport properties and critical exponent inequalities for random resistor and flow networks, Commun Math Phys, 105 (1986), 133-152.
    • (1986) Commun Math Phys , vol.105 , pp. 133-152
    • Chayes, J.T.1    Chayes, L.2
  • 12
    • 0007141651 scopus 로고
    • On the upper critical dimension in Bernoulli percolation
    • J. T. Chayes and L. Chayes, On the upper critical dimension in Bernoulli percolation, Commun Math Phys, 113 (1987), 27-48.
    • (1987) Commun Math Phys , vol.113 , pp. 27-48
    • Chayes, J.T.1    Chayes, L.2
  • 13
    • 0000028968 scopus 로고
    • The low-temperature behavior of disordered magnets
    • J. T. Chayes, L. Chayes, and J. Fröhlich, The low-temperature behavior of disordered magnets, Commun Math Phys, 100 (1985), 399-437.
    • (1985) Commun Math Phys , vol.100 , pp. 399-437
    • Chayes, J.T.1    Chayes, L.2    Fröhlich, J.3
  • 14
    • 4243944881 scopus 로고
    • Finite-size scaling and correlation lengths for disordered systems
    • J. T. Chayes, L. Chayes, D. Fisher, and T. Spencer, Finite-size scaling and correlation lengths for disordered systems, Phys Rev Lett, 57 (1986) 2999-3002.
    • (1986) Phys Rev Lett , vol.57 , pp. 2999-3002
    • Chayes, J.T.1    Chayes, L.2    Fisher, D.3    Spencer, T.4
  • 15
    • 0002809876 scopus 로고
    • The correlation length for the high-density phase of Bernoulli percolation
    • J. T. Chayes, L. Chayes, G. R. Grimmett, H. Kesten, and R. H. Schonmann, The correlation length for the high-density phase of Bernoulli percolation, Ann Probab, 17 (1989), 1277-1302.
    • (1989) Ann Probab , vol.17 , pp. 1277-1302
    • Chayes, J.T.1    Chayes, L.2    Grimmett, G.R.3    Kesten, H.4    Schonmann, R.H.5
  • 16
    • 0002181664 scopus 로고    scopus 로고
    • Independent and dependent percolation. Probability theory and applications
    • (Princeton, NJ, 1996), Amer. Math. Soc. Providence, RI
    • J. T. Chayes, A. Puha, and T. Sweet, Independent and dependent percolation. Probability theory and applications (Princeton, NJ, 1996), 49-166, IAS/Park City Math. Ser., Vol. 6, Amer. Math. Soc. Providence, RI (1999).
    • (1999) IAS/park City Math. Ser. , vol.6 , pp. 49-166
    • Chayes, J.T.1    Puha, A.2    Sweet, T.3
  • 17
    • 0002656525 scopus 로고
    • Shapes, surfaces and interfaces in percolation clusters
    • M. Daoud and N. Boccara (Editors), Springer-Verlag, Berlin
    • A. Coniglio, Shapes, surfaces and interfaces in percolation clusters, in Proc Les Houches Conf on Physics of Finely Divided Matter, M. Daoud and N. Boccara (Editors), Springer-Verlag, Berlin, 1985, 84-109.
    • (1985) Proc Les Houches Conf on Physics of Finely Divided Matter , pp. 84-109
    • Coniglio, A.1
  • 18
    • 0004246476 scopus 로고
    • Springer-Verlag, New York
    • G. Grimmett, Percolation, Springer-Verlag, New York, 1989.
    • (1989) Percolation
    • Grimmett, G.1
  • 19
    • 0001626028 scopus 로고
    • The supercritical phase of percolation is well behaved
    • G. R. Grimmett and J. M. Marstrand, The supercritical phase of percolation is well behaved, Proc Roy Soc London Ser A, 430 (1990), 439-457.
    • (1990) Proc Roy Soc London Ser A , vol.430 , pp. 439-457
    • Grimmett, G.R.1    Marstrand, J.M.2
  • 20
    • 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
  • 21
    • 0037757168 scopus 로고
    • On the time constant and path length of first passage percolation
    • H. Kesten, On the time constant and path length of first passage percolation, Adv Appl Probab, 12 (1980), 848-863.
    • (1980) Adv Appl Probab , vol.12 , pp. 848-863
    • Kesten, H.1
  • 23
    • 0001710365 scopus 로고
    • The incipient infinite cluster in two-dimensional percolation
    • H. Kesten, The incipient infinite cluster in two-dimensional percolation, Probab Theory Related Fields, 73 (1986), 369-394.
    • (1986) Probab Theory Related Fields , vol.73 , pp. 369-394
    • Kesten, H.1
  • 24
    • 0001755621 scopus 로고
    • Scaling relations for 2D-percolation
    • H. Kesten, Scaling relations for 2D-percolation, Commun Math Phys, 109 (1987), 109-156.
    • (1987) Commun Math Phys , vol.109 , pp. 109-156
    • Kesten, H.1
  • 25
    • 0002023496 scopus 로고
    • The probability of a large finite cluster in supercritical Bernoulli percolation
    • H. Kesten and Y. Zhang, The probability of a large finite cluster in supercritical Bernoulli percolation, Ann Probab, 18 (1990), 537-555.
    • (1990) Ann Probab , vol.18 , pp. 537-555
    • Kesten, H.1    Zhang, Y.2
  • 26
    • 0041049688 scopus 로고
    • Counting labelled trees
    • J. W. Moon, Counting labelled trees, Canad Math Monogr 1 (1970).
    • (1970) Canad Math Monogr , vol.1
    • Moon, J.W.1
  • 27
    • 0000040901 scopus 로고
    • Typical cluster size for two-dimensional percolation processes
    • B. Nguyen, Typical cluster size for two-dimensional percolation processes, J Statist Phys, 50 (1988), 715-726.
    • (1988) J Statist Phys , vol.50 , pp. 715-726
    • Nguyen, B.1
  • 28
    • 0042416901 scopus 로고    scopus 로고
    • Surface order large deviations for Ising, Potts and percolation models
    • A. Pisztora, Surface order large deviations for Ising, Potts and percolation models, Probab Theory Related Fields, 104 (1996), 427-466.
    • (1996) Probab Theory Related Fields , vol.104 , pp. 427-466
    • Pisztora, A.1
  • 29
    • 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
  • 30
    • 77957093986 scopus 로고
    • Percolation probabilities on the square lattice
    • P. D. Seymour and D. J. A. Welsh, Percolation probabilities on the square lattice, Ann Discrete Math, 3 (1978), 227-245.
    • (1978) Ann Discrete Math , vol.3 , pp. 227-245
    • Seymour, P.D.1    Welsh, D.J.A.2
  • 31
    • 0000176309 scopus 로고
    • Correlation inequalities and the decay of correlations in ferromagnets
    • B. Simon, Correlation inequalities and the decay of correlations in ferromagnets, Commun Math Phys, 77 (1980), 111-126.
    • (1980) Commun Math Phys , vol.77 , pp. 111-126
    • Simon, B.1
  • 32
    • 0040278746 scopus 로고
    • Hyperscaling inequalities for percolation
    • H. Tasaki, Hyperscaling inequalities for percolation, Commun Math Phys, 113 (1987), 49-65.
    • (1987) Commun Math Phys , vol.113 , pp. 49-65
    • Tasaki, H.1


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