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References

  • D. Ahlberg, H. Duminil-Copin, G. Kozma, and V. Sidoravicius, phSeven-dimensional forest fires, phAnn. Inst. Henri Poincaré Probab. Stat., to appear.
  • Aizenman, Michael; Grimmett, Geoffrey. Strict monotonicity for critical points in percolation and ferromagnetic models. J. Statist. Phys. 63 (1991), no. 5-6, 817--835. MR1116036
  • Aizenman, M.; Kesten, H.; Newman, C. M. Uniqueness of the infinite cluster and continuity of connectivity functions for short and long range percolation. Comm. Math. Phys. 111 (1987), no. 4, 505--531. MR0901151
  • Alexander, Kenneth S. Simultaneous uniqueness of infinite clusters in stationary random labeled graphs. Comm. Math. Phys. 168 (1995), no. 1, 39--55. MR1324390
  • Benjamini, Itai; Lyons, Russell; Peres, Yuval; Schramm, Oded. Critical percolation on any nonamenable group has no infinite clusters. Ann. Probab. 27 (1999), no. 3, 1347--1356. MR1733151
  • Benjamini, Itai; Schramm, Oded. Percolation beyond $Z^ d$, many questions and a few answers. Electron. Comm. Probab. 1 (1996), no. 8, 71--82 (electronic). MR1423907
  • van den Berg, J.; Brouwer, R. Self-destructive percolation. Random Structures Algorithms 24 (2004), no. 4, 480--501. MR2060632
  • van den Berg, J.; Brouwer, R.; Vogvolgyi, B. Box-crossings and continuity results for self-destructive percolation in the plane. In and out of equilibrium. 2, 117--135, Progr. Probab., 60, Birkhauser, Basel, 2008. MR2477379
  • van den Berg, J.; de Lima, B. N. B. Linear lower bounds for $\delta_ {\rm c}(p)$ for a class of 2D self-destructive percolation models. Random Structures Algorithms 34 (2009), no. 4, 520--526. MR2531782
  • Burton, R. M.; Keane, M. Density and uniqueness in percolation. Comm. Math. Phys. 121 (1989), no. 3, 501--505. MR0990777
  • Grimmett, G. R.; Newman, C. M. Percolation in $\infty+1$ dimensions. Disorder in physical systems, 167--190, Oxford Sci. Publ., Oxford Univ. Press, New York, 1990. MR1064560
  • Häggström, Olle; Jonasson, Johan. Uniqueness and non-uniqueness in percolation theory. Probab. Surv. 3 (2006), 289--344. MR2280297
  • Häggström, Olle; Peres, Yuval. Monotonicity of uniqueness for percolation on Cayley graphs: all infinite clusters are born simultaneously. Probab. Theory Related Fields 113 (1999), no. 2, 273--285. MR1676835
  • Harris, T. E. A lower bound for the critical probability in a certain percolation process. Proc. Cambridge Philos. Soc. 56 1960 13--20. MR0115221
  • Schonmann, Roberto H. Stability of infinite clusters in supercritical percolation. Probab. Theory Related Fields 113 (1999), no. 2, 287--300. MR1676831
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