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References

  • Berger, Noam. Transience, recurrence and critical behavior for long-range percolation. Comm. Math. Phys. 226 (2002), no. 3, 531--558. MR1896880
  • Benjamini, Itai; Berger, Noam. The diameter of long-range percolation clusters on finite cycles. Random Structures Algorithms 19 (2001), no. 2, 102--111. MR1848786
  • Biskup, Marek. On the scaling of the chemical distance in long-range percolation models. Ann. Probab. 32 (2004), no. 4, 2938--2977. MR2094435
  • Biskup, Marek. On the scaling of the chemical distance in long-range percolation models. Ann. Probab. 32 (2004), no. 4, 2938--2977. MR2094435
  • Friedli S., de Lima B.N.B., in preparation.
  • Fröhlich, Jürg; Spencer, Thomas. The phase transition in the one-dimensional Ising model with $1/r^{2}$ interaction energy. Comm. Math. Phys. 84 (1982), no. 1, 87--101. MR0660541
  • Grimmett, G. R.; Marstrand, J. M. The supercritical phase of percolation is well behaved. Proc. Roy. Soc. London Ser. A 430 (1990), no. 1879, 439--457. MR1068308
  • Kesten, Harry. Asymptotics in high dimensions for percolation. Disorder in physical systems, 219--240, Oxford Sci. Publ., Oxford Univ. Press, New York, 1990. MR1064563
  • Meester, Ronald; Steif, Jeffrey E. On the continuity of the critical value for long range percolation in the exponential case. Comm. Math. Phys. 180 (1996), no. 2, 483--504. MR1405960
  • Newman, C. M.; Schulman, L. S. One-dimensional $1/\vert j-i\vert ^ s$ percolation models: the existence of a transition for $s\leq 2$. Comm. Math. Phys. 104 (1986), no. 4, 547--571. MR0841669
  • Sidoravicius, V.; Surgailis, D.; Vares, M. E. On the truncated anisotropic long-range percolation on ${\bf Z}^ 2$. Stochastic Process. Appl. 81 (1999), no. 2, 337--349. MR1694537


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