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  • Aizenman, Michael. On the number of incipient spanning clusters. Nuclear Phys. B 485 (1997), no. 3, 551--582. MR1431856
  • 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
  • Fortuin, C. M.; Kasteleyn, P. W.; Ginibre, J. Correlation inequalities on some partially ordered sets. Comm. Math. Phys. 22 (1971), 89--103. MR0309498
  • 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
  • Hara, Takashi. Decay of correlations in nearest-neighbor self-avoiding walk, percolation, lattice trees and animals. Ann. Probab. 36 (2008), no. 2, 530--593. MR2393990
  • Járai, Antal A. Incipient infinite percolation clusters in 2D. Ann. Probab. 31 (2003), no. 1, 444--485. MR1959799
  • Kesten, Harry. Percolation theory for mathematicians. Progress in Probability and Statistics, 2. Birkhäuser, Boston, Mass., 1982. iv+423 pp. ISBN: 3-7643-3107-0 MR0692943
  • Demeter Kiss, Ioan Manolescu, and Vladas Sidoravicius, Planar lattices do not recover from forest fires, preprint, arxiv:1312.7004, 2013.
  • Kozma, Gady; Nachmias, Asaf. Arm exponents in high dimensional percolation. J. Amer. Math. Soc. 24 (2011), no. 2, 375--409. MR2748397
  • Morrow, G. J.; Zhang, Y. The sizes of the pioneering, lowest crossing and pivotal sites in critical percolation on the triangular lattice. Ann. Appl. Probab. 15 (2005), no. 3, 1832--1886. MR2152247
  • Nolin, Pierre. Near-critical percolation in two dimensions. Electron. J. Probab. 13 (2008), no. 55, 1562--1623. MR2438816
  • Russo, Lucio. On the critical percolation probabilities. Z. Wahrsch. Verw. Gebiete 56 (1981), no. 2, 229--237. MR0618273
  • Seymour, P. D.; Welsh, D. J. A. Percolation probabilities on the square lattice. Advances in graph theory (Cambridge Combinatorial Conf., Trinity College, Cambridge, 1977). Ann. Discrete Math. 3 (1978), 227--245. MR0494572
  • Smirnov, Stanislav; Werner, Wendelin. Critical exponents for two-dimensional percolation. Math. Res. Lett. 8 (2001), no. 5-6, 729--744. MR1879816
  • 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.; Conijn, R. P. The gaps between the sizes of large clusters in 2D critical percolation. Electron. Commun. Probab. 18 (2013), No. 92, 9 pp. MR3145048

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