The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off

References

  1. M. Aizenman and Ch. Newman. Tree graph inequalities and critical behavior in percolation models. J. Statist. Phys. 36 (1984), 107-143. Math. Review 86h:82045
  2. G. Grimmett. Percolation. Springer-Verlag (1999) Berlin, Second edition. Math. Review 2001a:60114
  3. T. Hara and G. Slade. Mean-field critical behaviour for percolation in high dimensions. Commun. Math. Phys. 128 (1990), 333-391. Math. Review 91a:82037
  4. M. Heydenreich, R. van der Hofstad and A. Sakai. Mean-field behavior for long- and finite range Ising model, percolation and self-avoiding walk. J. Statist. Phys. 132(6) (2008), 1001-1049. Math. Review 2009f:60116
  5. G. Kozma and A. Nachmias. The Alexander-Orbach conjecture holds in high dimensions. Invent. Math. 178(3) (2009), 635-654.
  6. G. Kozma. Percolation on a product of two trees. arXiv:1003.5240.
  7. G. Kozma. The triangle and the open triangle. To appear in Ann. Inst. Henri Poincar'e Probab. Stat. (2010). arXiv:0907.1959.
  8. R. Schonmann. Multiplicity of phase transitions and mean-field criticality on highly non-amenable graphs. Commun. Math. Phys. 219(2) (2001), 271-322. Math. Review 2002h:82036
  9. R. Schonmann. Mean-filed criticality for percolation on planar non-amenable graphs. Commun. Math. Phys. 225(3) (2002), 453-463. Math. Review 2003m:82039
  10. C. Wu. Critical behavior of percolation and Markov fields on branching planes. J. Appl. Probab. 30(3) (1993), 538-547. Math. Review 94g:60181
Bookmark and Share


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.