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References

  1. P. Bak, C. Tang, K.Wiesenfeld. Self-organized criticality. Phys. Rev. A (3) 38 (1988), no. 1, 364--374.
    2. MR0949160 (89g:58126)
  2. Benjamini, Itai, Lyons, Russell, Peres, Yuval, Schramm, Oded. Critical percolation on any nonamenable group has no infinite clusters. Ann. Prob. 27 (1999), no. 3, 1347--1356. MR1733151 (2000k:60197)
  3. D. Dhar. Studying self-organized criticality with exactly solved models, Arxiv, 1999. cond-mat/9909009.
  4. R. Dickman, M. Munoz, A. Vespagnani and S. Zapperi. Paths to self-organized criticality.  Brazilian Journal of Physics 30 (2000), 27-41.
  5. W. Feller. An introduction to probability theory and its applications. Vol. II. John Wiley & Sons, Inc., New York-London-Sydney 1966 xviii+636 pp. MR0210154 (35 #1048)
  6. A. Fey-den Boer, R. Meester, C. Quant, F. Redig. A probabilistic approach to Zhang's sandpile model,  Comm. Math. Phys. 280 (2) (2008), 351-388.
  7. A. Fey-den Boer, R. Meester, F. Redig. (2008) Stabilizability and percolation in the infinite volume sandpile model. To appear in Annals of Probability.
  8. A. Fey-den Boer, F. Redig. Organized versus self-organized criticality in the abelian sandpile model. Markov Process. Related Fields 11 (2005), no. 3, 425--442. MR2175021 (2006g:60136)
  9. I.M. Janosi. Effect of anisotropy on the self-organized critical state. Phys. Rev. A 42 (2) (1989), 769-774.
  10. R. Meester, C. Quant. Connections between `self-organised' and `classical' criticality. Markov Process. Related Fields 11 (2005), no. 2, 355--370. MR2150148 ((2006d:82054)
  11. R. Meester, F. Redig, D. Znamenski. The abelian sandpile: a mathematical introduction. Markov Process. Related Fields 7 (2001), no. 4, 509--523. MR1893138 ((2003f:60175)
  12. J.R. Norris. Markov chains. Reprint of 1997 original. Cambridge Series in Statistical and Probabilistic Mathematics, 2. Cambridge University Press, Cambridge, 1998. xvi+237 pp. ISBN: 0-521-48181-3 MR1600720 ((99c:60144)
  13. H. Thorisson. Coupling, stationarity, and regeneration. Probability and its Applications (New York). Springer-Verlag, New York, 2000. xiv+517 pp. ISBN: 0-387-98779-7 MR1741181 (2001b:60003)
  14. Y.-C. Zhang. Scaling theory of Self-Organized Criticality. Phys. Rev. Lett. 63 (5) (1989), 470-473.

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