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

  • J. van den Berg and A. Gandolfi (2012), BK-type inequalities and generalized random-cluster representations. Available at http://arxiv.org/pdf/1203.3665v1.pdf
  • van den Berg, J. Sharpness of the percolation transition in the two-dimensional contact process. Ann. Appl. Probab. 21 (2011), no. 1, 374--395. MR2778387 http://arxiv.org/pdf/1105.3862.pdf
  • van den Berg, J.; Kesten, H. Inequalities with applications to percolation and reliability. J. Appl. Probab. 22 (1985), no. 3, 556--569. MR0799280
  • Borcea, Julius; Brändén, Petter; Liggett, Thomas M. Negative dependence and the geometry of polynomials. J. Amer. Math. Soc. 22 (2009), no. 2, 521--567. MR2476782
  • Jonasson, Johan. Mixing time bounds for overlapping cycles shuffles. Electron. J. Probab. 16 (2011), no. 46, 1281--1295. MR2827459
  • Dubhashi, Devdatt; Jonasson, Johan; Ranjan, Desh. Positive influence and negative dependence. Combin. Probab. Comput. 16 (2007), no. 1, 29--41. MR2286510
  • Dubhashi, Devdatt; Ranjan, Desh. Balls and bins: a study in negative dependence. Random Structures Algorithms 13 (1998), no. 2, 99--124. MR1642566
  • Grimmett, Geoffrey. Percolation. Second edition. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 321. Springer-Verlag, Berlin, 1999. xiv+444 pp. ISBN: 3-540-64902-6 MR1707339
  • Markström, Klas. Closure properties and negatively associated measures violating the van den Berg-Kesten inequality. Electron. Commun. Probab. 15 (2010), 449--456. MR2726091
  • Pemantle, Robin. Towards a theory of negative dependence. Probabilistic techniques in equilibrium and nonequilibrium statistical physics. J. Math. Phys. 41 (2000), no. 3, 1371--1390. MR1757964
  • Reimer, David. Proof of the van den Berg-Kesten conjecture. Combin. Probab. Comput. 9 (2000), no. 1, 27--32. MR1751301


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