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Analyticity properties and power law estimates of functions in percolation theory. (English) Zbl 0512.60095

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
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[1] M. E. Fisher, Critical Probabilities for Cluster Size and Percolation Problems,J. Math. Phys. 2:620-627 (1961). · Zbl 0105.43602 · doi:10.1063/1.1703746
[2] M. E. Fisher and J. W. Essam, Some Cluster Size and Percolation Problems,J. Math. Phys. 2:609-619 (1961). · Zbl 0105.43601 · doi:10.1063/1.1703745
[3] S. R. Broadbent and J. M. Hammersley, Percolation Processes,Proc. Cambridge Philos. Soc. 53:629-641, 642-645 (1957). · Zbl 0091.13901 · doi:10.1017/S0305004100032680
[4] P. D. Seymour and D. J. A. Welsh, Percolation Probabilities on the Square Lattice,Ann. Discrete Math. 3:227-245 (1978). · Zbl 0405.60015 · doi:10.1016/S0167-5060(08)70509-0
[5] R. T. Smythe and J. C. Wierman,First-Passage Percolation on the Square Lattice, Vol. 671 inLecture Notes in Math (Springer-Verlag, New York, 1978). · Zbl 0379.60001
[6] L. Russo, A Note on Percolation,Z. Wahrscheinlichkeitstheorie verw. Geb. 43:39-48 (1978). · Zbl 0363.60120 · doi:10.1007/BF00535274
[7] H. Kesten, The Critical Probability of Bond Percolation on the Square Lattice Equals 1/2,Commun. Math. Phys. 74:41-59 (1980). · Zbl 0441.60010 · doi:10.1007/BF01197577
[8] L. Russo, On the Critical Percolation Probabilities,Z. Wahrscheinlichkeitstheorie verw. Geb. (1981). · Zbl 0457.60084
[9] J. C. Wierman, Bond Percolation on Honeycomb and Triangular Lattices,Adv. Appl. Prob., to appear. · Zbl 0457.60085
[10] D. Griffeath, The Basic Contact Process,Stoch. Proc. Appl. 11:151-185 (1981). · Zbl 0463.60085 · doi:10.1016/0304-4149(81)90002-8
[11] M. F. Sykes and J. W. Essam, Exact Critical Percolation Probabilities for Site and Bond Problems in Two Dimensions,J. Math. Phys. 5:1117-1127 (1964). · doi:10.1063/1.1704215
[12] G. R. Grimmett, On the Number of Clusters in the Percolation Model,J. London Math. Soc. (2)13:346-350 (1976). · Zbl 0338.60034 · doi:10.1112/jlms/s2-13.2.346
[13] J. C. Wierman, On Critical Probabilities in Percolation Theory,J. Math. Phys. 19:1979-1982 (1978). · Zbl 0416.60099 · doi:10.1063/1.523894
[14] J. W. Essam and K. M. Gwilym, The Scaling Laws for Percolation Processes,J. Phys. C 4:L228-L232(1971). · doi:10.1088/0022-3719/4/10/015
[15] C. Domb, Lattice Animals and Percolation,J. Phys. A 9:L141-L148 (1976). · doi:10.1088/0305-4470/9/10/005
[16] D. Stauffer, Scaling Theory of Percolation Clusters,Phys. Rep. 54:1-74 (1979). · doi:10.1016/0370-1573(79)90060-7
[17] D. Payandeh, A Block Cluster Approach to Percolation,Riv. Nuovo Cimento Ser. 3 3(3):(1980) [see alsoPhys. Rev. B 20:1285-1287 (1979)].
[18] T. E. Harris, A Lower Bound for the Critical Probability in a Certain Percolation Process,Proc. Cambridge Philos. Soc. 56:13-20 (1960). · Zbl 0122.36403 · doi:10.1017/S0305004100034241
[19] H. Kunz and B. Souillard, Essential Singularity in Percolation Problems and Asymptotic Behavior of Cluster Size Distribution,J. Stat. Phys. 19:77-106 (1978). · doi:10.1007/BF01020335
[20] H. Kesten, On the Time Constant and Path Length of First-Passage Percolation,Adv. Appl. Prob. 12:848-863 (1980). · Zbl 0436.60077 · doi:10.2307/1426744
[21] G. R. Grimmett, On the Differentiability of the Number of Clusters per Vertex in the Percolation Model,J. London Math Soc. (2)23:372-384 (1981). · Zbl 0497.60010 · doi:10.1112/jlms/s2-23.2.372
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