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

  • van den Berg, J.; Conijn, R. On the size of the largest cluster in $2D$ critical percolation. Electron. Commun. Probab. 17 (2012), no. 58, 13 pp. MR3005731
  • van den Berg, J.; Kesten, H. Inequalities with applications to percolation and reliability. J. Appl. Probab. 22 (1985), no. 3, 556--569. MR0799280
  • Bollobás, Béla; Riordan, Oliver. Percolation. Cambridge University Press, New York, 2006. x+323 pp. ISBN: 978-0-521-87232-4; 0-521-87232-4 MR2283880
  • Borgs, C.; Chayes, J. T.; Kesten, H.; Spencer, J. Uniform boundedness of critical crossing probabilities implies hyperscaling. Statistical physics methods in discrete probability, combinatorics, and theoretical computer science (Princeton, NJ, 1997). Random Structures Algorithms 15 (1999), no. 3-4, 368--413. MR1716769
  • Borgs, C.; Chayes, J. T.; Kesten, H.; Spencer, J. The birth of the infinite cluster: finite-size scaling in percolation. Dedicated to Joel L. Lebowitz. Comm. Math. Phys. 224 (2001), no. 1, 153--204. MR1868996
  • Le Cam, Lucien. On the distribution of sums of independent random variables. 1965 Proc. Internat. Res. Sem., Statist. Lab., Univ. California, Berkeley, Calif. pp. 179--202 Springer-Verlag, New York MR0199871
  • Esseen, C. G. On the concentration function of a sum of independent random variables. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 9 1968 290--308. MR0231419
  • Garban, Christophe; Pete, Gábor; Schramm, Oded. Pivotal, cluster, and interface measures for critical planar percolation. J. Amer. Math. Soc. 26 (2013), no. 4, 939--1024. MR3073882
  • 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
  • Járai, Antal A. Incipient infinite percolation clusters in 2D. Ann. Probab. 31 (2003), no. 1, 444--485. MR1959799
  • Kesten, Harry. The incipient infinite cluster in two-dimensional percolation. Probab. Theory Related Fields 73 (1986), no. 3, 369--394. MR0859839


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