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


  • Aizenman, M.; Lebowitz, J. L. Metastability effects in bootstrap percolation. J. Phys. A 21 (1988), no. 19, 3801--3813. MR0968311
  • Balogh, József; Bollobás, Bála; Duminil-Copin, Hugo; Morris, Robert. The sharp threshold for bootstrap percolation in all dimensions. Trans. Amer. Math. Soc. 364 (2012), no. 5, 2667--2701. MR2888224
  • Balogh, József; Bollobás, Bála; Morris, Robert. Bootstrap percolation in high dimensions. Combin. Probab. Comput. 19 (2010), no. 5-6, 643--692. MR2726074
  • Balogh, József; Peres, Yuval; Pete, Gábor. Bootstrap percolation on infinite trees and non-amenable groups. Combin. Probab. Comput. 15 (2006), no. 5, 715--730. MR2248323
  • Balogh, József; Pittel, Boris G. Bootstrap percolation on the random regular graph. Random Structures Algorithms 30 (2007), no. 1-2, 257--286. MR2283230
  • Biskup, Marek; Schonmann, Roberto H. Metastable behavior for bootstrap percolation on regular trees. J. Stat. Phys. 136 (2009), no. 4, 667--676. MR2540158
  • J. Chalupa, P.L. Leath, and G.R. Reich, Bootstrap percolation on a Bethe latice, J. Phys. C 12 (1979), L31--L35.
  • Fontes, L. R. G.; Schonmann, R. H. Bootstrap percolation on homogeneous trees has 2 phase transitions. J. Stat. Phys. 132 (2008), no. 5, 839--861. MR2430783
  • Gautschi, Walter. Some elementary inequalities relating to the gamma and incomplete gamma function. J. Math. and Phys. 38 1959/60 77--81. MR0103289
  • K. Gunderson and M. Przykucki, Lower bounds for bootstrap percolation on Galton--Watson trees, in preparation.
  • Holroyd, Alexander E. Sharp metastability threshold for two-dimensional bootstrap percolation. Probab. Theory Related Fields 125 (2003), no. 2, 195--224. MR1961342
  • Janson, Svante. On percolation in random graphs with given vertex degrees. Electron. J. Probab. 14 (2009), no. 5, 87--118. MR2471661
  • Janson, Svante; Łuczak, Tomasz; Turova, Tatyana; Vallier, Thomas. Bootstrap percolation on the random graph $G_ {n,p}$. Ann. Appl. Probab. 22 (2012), no. 5, 1989--2047. MR3025687
  • Lyons, Russell. Random walks and percolation on trees. Ann. Probab. 18 (1990), no. 3, 931--958. MR1062053
  • R. Lyons and Y. Peres, Probability on trees and networks, 2012, In preparation. Current version available at

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