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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)
     

The triangle condition for percolation

Author(s): Takashi Hara; Gordon Slade
Journal: Bull. Amer. Math. Soc. 21 (1989), 269-273.
MSC (1985): Primary 82A43, 60K35
MathSciNet review: 992514
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References:

1.
M. Aizenman, Geometric analysis of φ, Comm. Math. Phys. 86 (1982), 1-48. MR 678000
2.
M. Aizenman and D. J. Barsky, Sharpness of the phase transition in percolation models, Comm. Math. Phys. 108 (1987), 489-526. MR 874906
3.
M. Aizenman, H. Kesten and C. M. Newman, Uniqueness of the infinite cluster and continuity of connectivity functions for short and long range percolation, Comm. Math. Phys. 111 (1987), 505-531. MR 901151
4.
M. Aizenman and C. M. Newman, Tree graph inequalities and critical behaviour in percolation models, J. Statist. Phys. 36 (1984), 107-143. MR 762034
5.
D. Barsky and M. Aizenman, Percolation critical exponents under the triangle condition, preprint (1988). MR 1127713
6.
J. van den Berg and H. Kesten, Inequalities with applications to percolation and reliability, J. Appl. Prob. 22 (1985), 556-569. MR 799280
7.
A. Bovier, G. Felder and J. Fröhlich, On the critical properties of the Edwards and the selfavoiding walk model of polymer chains, Nucl. Phys. B230 [FS210] (1984), 119-147. MR 729794
8.
S. R. Broadbent and J. M. Hammersley, Percolation processes. I. Crystals and mazes, Proc. Cambridge Philos. Soc. 53 (1957), 629-641; J. M. Hammersley: Percolation processes. II. The Connectivity constant, ibid, 642-645. MR 91567
9.
D. Brydges and T. Spencer, Self-avoiding walk in 5 or more dimensions, Comm. Math. Phys. 97 (1985), 125-148. MR 782962
10.
J. T. Chayes and L. Chayes, On the upper critical dimension of Bernoulli percolation, Comm. Math. Phys. 113 (1987), 27-48. MR 918403
11.
J. M. Hammersley, Bornes supérieures de la probabilité critique dans un processus defiltration, Le Calcul des Probabilités et ses Applications, CNRS, Paris, 1959, pp. 17-37. MR 105751
12.
T. Hara, Mean field critical behaviour of correlation length for percolation in high dimensions (in preparation).
13.
T. Hara and G. Slade, Mean field critical phenomena for percolation in high dimensions, preprint (1989). MR 1033813
14.
T. Hara and G. Slade, On the upper critical dimension of lattice trees and lattice animals (in preparation).
15.
H. Kesten, Percolation theory and first passage percolation, Ann. Probab. 15 (1987), 1231-1271. MR 905330
16.
M. V. Menshikov, S. A. Molchanov and A. F. Sidorenko, Percolation theory and some applications, Itogi Nauki i Tekhniki (Series of Probability Theory, Mathematical Statistics, Theoretical Cybernetics) 24 (1986), 53-110; English Translation: J. Soviet Math. 42 (1988), 1766-1810. MR 865158
17.
B. G. Nguyen, Gap exponents for percolation processes with triangle condition, J. Statist. Phys. 49 (1987), 235-243. MR 923855
18.
L. Russo, On the critical percolation probabilities, Z. Wahrsch. Verw. Gebiete 56 (1981), 229-237. MR 618273
19.
G. Slade, The diffusion of self-avoiding random walk in high dimensions, Comm. Math. Phys. 110(1987), 661-683. MR 895223
20.
D. Stauffer, Introduction to percolation theory, Taylor and Francis, London and Philadelphia, 1985. MR 849782
21.
H. Tasaki, Hyperscaling inequalities for percolation, Comm. Math. Phys. 113 (1987), 49-65. MR 918404

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Additional Information:

DOI: 10.1090/S0273-0979-1989-15827-8
PII: S 0273-0979(1989)15827-8


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