References
- M. Aizenman, C. M. Newman, Discontinuity of the percolation density in one-dimensional 1/∣ x - y ∣2 percolation models. Comm. Math. Phys., Vol. 107, 1986, pp. 611–647.
- S. R. Athreya, J. M. Swart, Survival of contact processes on the hierarchical group. Probab. Theory Relat. Fields, Vol. 147, 2010, pp. 529–563.
- A. L. Barab′asi, E. Ravaz, Hierarchical organization in complex networks. Phys. Rev. E, Vol. 67, 2003, 026112.
- I. Benjamini, O. Schramm, Percolation beyond ℤd, many questions and a few answers. Elect. Commun. Probab., Vol. 1, 1996, pp. 71–82.
- N. Berger, Transience, recurrence and critical behavior for long-range percolation. Comm. Math. Phys., Vol. 226, 2002, pp. 531–558.
- M. Biskup, On the scaling of chemical distance in long-range percoaltion models. Ann. Probab., Vol. 32, 2004, pp. 2938–2977.
- D. Coppersmith, D. Gamarnik, and M. Sviridenko, The diameter of a long-range percolation graph. Random Struct. Algorithms, Vol. 21, 2002, pp. 1–13.
- D. A. Dawson, and L. G. Gorostiza, Percolation in an ultrametric space. arXiv:1006.4400v2, 2011.
- D. A. Dawson, and L. G. Gorostiza, Percolation in a hierarchical random graph. Comm. Stochastic Analysis, Vol. 1, 2007, pp. 29–47.
- G. Grimmett, Percolation. Springer, New York, 1999.
- V. Koval, R. Meester, and P. Trapman, Long-range percolation on the hierarchical lattice, Electron. J. Probob, Vol. 17(57), 2012.
- R. Rammal, G. Toulouse, M. A. Virasoro, Ultrametricity for physicists. Rev. Mod. Phys., Vol. 58, 1986, pp. 765–788.
- P. Schneider, Nonarchimedean Functional Analysis. Springer, New York, 2002.
- L. S. Schulman, Long range percolation in one dimension. J. Phys. A: Math. Gen., Vol. 16, 1983, pp. L639–L641.
- Y. Shang, Percolation in a hierarchical lattice. Z. Naturforsch. A, Vol. 67, 2012, pp. 225–229.
- Y. Shang, Multi-type directed scale-free percolation. Commun. Theor. Phys., Vol. 57, 2012, pp. 701–716.
- Y. Shang, The sizes of large hierarchical long-range percolation clusters. World Acad. Sci. Eng. Technol., Vol. 56, 2011, pp. 1440–1443.
- Y. Shang, W. Luo, S. Xu, L-hop percolation on networks with arbitrary degree distributions and its applications. Phys. Rev. E, Vol. 84, 2011, 031113.
- P. Trapman, The growth of the infinite long-range percolation cluster. Ann. Probab., Vol. 38, 2010, pp. 1583–1608.